Results of Airy and Related Functions

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
9.2.E2	${\displaystyle{\displaystyle w=\mathrm{Ai}\left(z\right),\;\mathrm{Bi}\left(z\right),\;\mathrm{Ai}\left(ze^{-2\pi\mathrm{i}/3}\right)}}$	w = AiryAi(z), AiryBi(z), AiryAi(z*exp(- 2*Pi*I/ 3))	w = AiryAi[z], AiryBi[z], AiryAi[z*Exp[- 2*Pi*I/ 3]]	Failure	Failure	Error	Error
9.2.E2	${\displaystyle{\displaystyle w=\mathrm{Ai}\left(z\right),\;\mathrm{Bi}\left(z\right),\;\mathrm{Ai}\left(ze^{+2\pi\mathrm{i}/3}\right)}}$	w = AiryAi(z), AiryBi(z), AiryAi(z*exp(+ 2*Pi*I/ 3))	w = AiryAi[z], AiryBi[z], AiryAi[z*Exp[+ 2*Pi*I/ 3]]	Failure	Failure	Error	Error
9.2.E3	${\displaystyle{\displaystyle\mathrm{Ai}\left(0\right)=\frac{1}{3^{2/3}\Gamma\left(\tfrac{2}{3}\right)}}}$	AiryAi(0)=(1)/((3)^(2/ 3)* GAMMA((2)/(3)))	AiryAi[0]=Divide[1,(3)^(2/ 3)* Gamma[Divide[2,3]]]	Successful	Successful	-	-
9.2.E4	${\displaystyle{\displaystyle\mathrm{Ai}'\left(0\right)=-\frac{1}{3^{1/3}\Gamma\left(\tfrac{1}{3}\right)}}}$	subs( temp=0, diff( AiryAi(temp), temp$(1) ) )= -(1)/((3)^(1/ 3)* GAMMA((1)/(3)))	(D[AiryAi[temp], {temp, 1}]/.temp-> 0)= -Divide[1,(3)^(1/ 3)* Gamma[Divide[1,3]]]	Successful	Successful	-	-
9.2.E5	${\displaystyle{\displaystyle\mathrm{Bi}\left(0\right)=\frac{1}{3^{1/6}\Gamma\left(\tfrac{2}{3}\right)}}}$	AiryBi(0)=(1)/((3)^(1/ 6)* GAMMA((2)/(3)))	AiryBi[0]=Divide[1,(3)^(1/ 6)* Gamma[Divide[2,3]]]	Successful	Successful	-	-
9.2.E6	${\displaystyle{\displaystyle\mathrm{Bi}'\left(0\right)=\frac{3^{1/6}}{\Gamma\left(\tfrac{1}{3}\right)}}}$	subs( temp=0, diff( AiryBi(temp), temp$(1) ) )=((3)^(1/ 6))/(GAMMA((1)/(3)))	(D[AiryBi[temp], {temp, 1}]/.temp-> 0)=Divide[(3)^(1/ 6),Gamma[Divide[1,3]]]	Successful	Successful	-	-
9.2.E7	${\displaystyle{\displaystyle\mathscr{W}\left\{\mathrm{Ai}\left(z\right),\mathrm{Bi}\left(z\right)\right\}=\frac{1}{\pi}}}$	(AiryAi(z))*diff(AiryBi(z), z)-diff(AiryAi(z), z)*(AiryBi(z))=(1)/(Pi)	Wronskian[{AiryAi[z], AiryBi[z]}, z]=Divide[1,Pi]	Failure	Successful	Successful	-
9.2.E8	${\displaystyle{\displaystyle\mathscr{W}\left\{\mathrm{Ai}\left(z\right),\mathrm{Ai}\left(ze^{-2\pi i/3}\right)\right\}=\frac{e^{+\pi i/6}}{2\pi}}}$	(AiryAi(z))*diff(AiryAi(z*exp(- 2*Pi*I/ 3)), z)-diff(AiryAi(z), z)*(AiryAi(z*exp(- 2*Pi*I/ 3)))=(exp(+ Pi*I/ 6))/(2*Pi)	Wronskian[{AiryAi[z], AiryAi[z*Exp[- 2*Pi*I/ 3]]}, z]=Divide[Exp[+ Pi*I/ 6],2*Pi]	Failure	Successful	Successful	-
9.2.E8	${\displaystyle{\displaystyle\mathscr{W}\left\{\mathrm{Ai}\left(z\right),\mathrm{Ai}\left(ze^{+2\pi i/3}\right)\right\}=\frac{e^{-\pi i/6}}{2\pi}}}$	(AiryAi(z))*diff(AiryAi(z*exp(+ 2*Pi*I/ 3)), z)-diff(AiryAi(z), z)*(AiryAi(z*exp(+ 2*Pi*I/ 3)))=(exp(- Pi*I/ 6))/(2*Pi)	Wronskian[{AiryAi[z], AiryAi[z*Exp[+ 2*Pi*I/ 3]]}, z]=Divide[Exp[- Pi*I/ 6],2*Pi]	Failure	Successful	Successful	-
9.2.E9	${\displaystyle{\displaystyle\mathscr{W}\left\{\mathrm{Ai}\left(ze^{-2\pi i/3}\right),\mathrm{Ai}\left(ze^{2\pi i/3}\right)\right\}=\frac{1}{2\pi i}}}$	(AiryAi(z*exp(- 2*Pi*I/ 3)))*diff(AiryAi(z*exp(2*Pi*I/ 3)), z)-diff(AiryAi(z*exp(- 2*Pi*I/ 3)), z)*(AiryAi(z*exp(2*Pi*I/ 3)))=(1)/(2*Pi*I)	Wronskian[{AiryAi[z*Exp[- 2*Pi*I/ 3]], AiryAi[z*Exp[2*Pi*I/ 3]]}, z]=Divide[1,2*Pi*I]	Failure	Successful	Successful	-
9.2.E10	${\displaystyle{\displaystyle\mathrm{Bi}\left(z\right)=e^{-\pi i/6}\mathrm{Ai}\left(ze^{-2\pi i/3}\right)+e^{\pi i/6}\mathrm{Ai}\left(ze^{2\pi i/3}\right)}}$	AiryBi(z)= exp(- Pi*I/ 6)*AiryAi(z*exp(- 2*Pi*I/ 3))+ exp(Pi*I/ 6)*AiryAi(z*exp(2*Pi*I/ 3))	AiryBi[z]= Exp[- Pi*I/ 6]*AiryAi[z*Exp[- 2*Pi*I/ 3]]+ Exp[Pi*I/ 6]*AiryAi[z*Exp[2*Pi*I/ 3]]	Failure	Successful	Successful	-
9.2.E11	${\displaystyle{\displaystyle\mathrm{Ai}\left(ze^{-2\pi i/3}\right)=\tfrac{1}{2}e^{-\pi i/3}\left(\mathrm{Ai}\left(z\right)+i\mathrm{Bi}\left(z\right)\right)}}$	AiryAi(z*exp(- 2*Pi*I/ 3))=(1)/(2)*exp(- Pi*I/ 3)*(AiryAi(z)+ I*AiryBi(z))	AiryAi[z*Exp[- 2*Pi*I/ 3]]=Divide[1,2]*Exp[- Pi*I/ 3]*(AiryAi[z]+ I*AiryBi[z])	Failure	Successful	Successful	-
9.2.E11	${\displaystyle{\displaystyle\mathrm{Ai}\left(ze^{+2\pi i/3}\right)=\tfrac{1}{2}e^{+\pi i/3}\left(\mathrm{Ai}\left(z\right)-i\mathrm{Bi}\left(z\right)\right)}}$	AiryAi(z*exp(+ 2*Pi*I/ 3))=(1)/(2)*exp(+ Pi*I/ 3)*(AiryAi(z)- I*AiryBi(z))	AiryAi[z*Exp[+ 2*Pi*I/ 3]]=Divide[1,2]*Exp[+ Pi*I/ 3]*(AiryAi[z]- I*AiryBi[z])	Failure	Successful	Successful	-
9.2.E12	${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)+e^{-2\pi i/3}\mathrm{Ai}\left(ze^{-2\pi i/3}\right)+e^{2\pi i/3}\mathrm{Ai}\left(ze^{2\pi i/3}\right)=0}}$	AiryAi(z)+ exp(- 2*Pi*I/ 3)*AiryAi(z*exp(- 2*Pi*I/ 3))+ exp(2*Pi*I/ 3)*AiryAi(z*exp(2*Pi*I/ 3))= 0	AiryAi[z]+ Exp[- 2*Pi*I/ 3]*AiryAi[z*Exp[- 2*Pi*I/ 3]]+ Exp[2*Pi*I/ 3]*AiryAi[z*Exp[2*Pi*I/ 3]]= 0	Failure	Successful	Successful	-
9.2.E13	${\displaystyle{\displaystyle\mathrm{Bi}\left(z\right)+e^{-2\pi i/3}\mathrm{Bi}\left(ze^{-2\pi i/3}\right)+e^{2\pi i/3}\mathrm{Bi}\left(ze^{2\pi i/3}\right)=0}}$	AiryBi(z)+ exp(- 2*Pi*I/ 3)*AiryBi(z*exp(- 2*Pi*I/ 3))+ exp(2*Pi*I/ 3)*AiryBi(z*exp(2*Pi*I/ 3))= 0	AiryBi[z]+ Exp[- 2*Pi*I/ 3]*AiryBi[z*Exp[- 2*Pi*I/ 3]]+ Exp[2*Pi*I/ 3]*AiryBi[z*Exp[2*Pi*I/ 3]]= 0	Failure	Successful	Successful	-
9.2.E14	${\displaystyle{\displaystyle\mathrm{Ai}\left(-z\right)=e^{\pi i/3}\mathrm{Ai}\left(ze^{\pi i/3}\right)+e^{-\pi i/3}\mathrm{Ai}\left(ze^{-\pi i/3}\right)}}$	AiryAi(- z)= exp(Pi*I/ 3)*AiryAi(z*exp(Pi*I/ 3))+ exp(- Pi*I/ 3)*AiryAi(z*exp(- Pi*I/ 3))	AiryAi[- z]= Exp[Pi*I/ 3]*AiryAi[z*Exp[Pi*I/ 3]]+ Exp[- Pi*I/ 3]*AiryAi[z*Exp[- Pi*I/ 3]]	Failure	Successful	Successful	-
9.2.E15	${\displaystyle{\displaystyle\mathrm{Bi}\left(-z\right)=e^{-\pi i/6}\mathrm{Ai}\left(ze^{\pi i/3}\right)+e^{\pi i/6}\mathrm{Ai}\left(ze^{-\pi i/3}\right)}}$	AiryBi(- z)= exp(- Pi*I/ 6)*AiryAi(z*exp(Pi*I/ 3))+ exp(Pi*I/ 6)*AiryAi(z*exp(- Pi*I/ 3))	AiryBi[- z]= Exp[- Pi*I/ 6]*AiryAi[z*Exp[Pi*I/ 3]]+ Exp[Pi*I/ 6]*AiryAi[z*Exp[- Pi*I/ 3]]	Failure	Successful	Successful	-
9.5.E1	${\displaystyle{\displaystyle\mathrm{Ai}\left(x\right)=\frac{1}{\pi}\int_{0}^{\infty}\cos\left(\tfrac{1}{3}t^{3}+xt\right)\mathrm{d}t}}$	AiryAi(x)=(1)/(Pi)*int(cos((1)/(3)*(t)^(3)+ x*t), t = 0..infinity)	AiryAi[x]=Divide[1,Pi]*Integrate[Cos[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}]	Successful	Failure	-	Successful
9.5.E2	${\displaystyle{\displaystyle\mathrm{Ai}\left(-x\right)=\frac{x^{\ifrac{1}{2}}}{\pi}\int_{-1}^{\infty}\cos\left(x^{\ifrac{3}{2}}(\tfrac{1}{3}t^{3}+t^{2}-\tfrac{2}{3})\right)\mathrm{d}t}}$	AiryAi(- x)=((x)^((1)/(2)))/(Pi)*int(cos((x)^((3)/(2))*((1)/(3)*(t)^(3)+ (t)^(2)-(2)/(3))), t = - 1..infinity)	AiryAi[- x]=Divide[(x)^(Divide[1,2]),Pi]*Integrate[Cos[(x)^(Divide[3,2])*(Divide[1,3]*(t)^(3)+ (t)^(2)-Divide[2,3])], {t, - 1, Infinity}]	Failure	Failure	Skip	Error
9.5.E3	${\displaystyle{\displaystyle\mathrm{Bi}\left(x\right)=\frac{1}{\pi}\int_{0}^{\infty}\exp\left(-{\tfrac{1}{3}}t^{3}+xt\right)\mathrm{d}t+\frac{1}{\pi}\int_{0}^{\infty}\sin\left(\tfrac{1}{3}t^{3}+xt\right)\mathrm{d}t}}$	AiryBi(x)=(1)/(Pi)*int(exp(-(1)/(3)*(t)^(3)+ x*t), t = 0..infinity)+(1)/(Pi)*int(sin((1)/(3)*(t)^(3)+ x*t), t = 0..infinity)	AiryBi[x]=Divide[1,Pi]*Integrate[Exp[-Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}]+Divide[1,Pi]*Integrate[Sin[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}]	Failure	Failure	Skip	Successful
9.5.E4	${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{1}{2\pi i}\int_{\infty e^{-\pi i/3}}^{\infty e^{\pi i/3}}\exp\left(\tfrac{1}{3}t^{3}-zt\right)\mathrm{d}t}}$	AiryAi(z)=(1)/(2*Pi*I)*int(exp((1)/(3)*(t)^(3)- z*t), t = infinity*exp(- Pi*I/ 3)..infinity*exp(Pi*I/ 3))	AiryAi[z]=Divide[1,2*Pi*I]*Integrate[Exp[Divide[1,3]*(t)^(3)- z*t], {t, Infinity*Exp[- Pi*I/ 3], Infinity*Exp[Pi*I/ 3]}]	Failure	Failure	Skip	Skip
9.5.E5	${\displaystyle{\displaystyle\mathrm{Bi}\left(z\right)=\frac{1}{2\pi}\int_{-\infty}^{\infty e^{\pi i/3}}\exp\left(\tfrac{1}{3}t^{3}-zt\right)\mathrm{d}t+\dfrac{1}{2\pi}\int_{-\infty}^{\infty e^{-\pi i/3}}\exp\left(\tfrac{1}{3}t^{3}-zt\right)\mathrm{d}t}}$	AiryBi(z)=(1)/(2*Pi)*int(exp((1)/(3)*(t)^(3)- z*t), t = - infinity..infinity*exp(Pi*I/ 3))+(1)/(2*Pi)*int(exp((1)/(3)*(t)^(3)- z*t), t = - infinity..infinity*exp(- Pi*I/ 3))	AiryBi[z]=Divide[1,2*Pi]*Integrate[Exp[Divide[1,3]*(t)^(3)- z*t], {t, - Infinity, Infinity*Exp[Pi*I/ 3]}]+Divide[1,2*Pi]*Integrate[Exp[Divide[1,3]*(t)^(3)- z*t], {t, - Infinity, Infinity*Exp[- Pi*I/ 3]}]	Failure	Failure	Skip	Skip
9.5.E6	${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{\sqrt{3}}{2\pi}\int_{0}^{\infty}\exp\left(-\frac{t^{3}}{3}-\frac{z^{3}}{3t^{3}}\right)\mathrm{d}t}}$	AiryAi(z)=(sqrt(3))/(2*Pi)*int(exp(-((t)^(3))/(3)-((z)^(3))/(3*(t)^(3))), t = 0..infinity)	AiryAi[z]=Divide[Sqrt[3],2*Pi]*Integrate[Exp[-Divide[(t)^(3),3]-Divide[(z)^(3),3*(t)^(3)]], {t, 0, Infinity}]	Successful	Failure	-	Successful
9.5.E7	${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{e^{-\zeta}}{\pi}\int_{0}^{\infty}\exp\left(-z^{\ifrac{1}{2}}t^{2}\right)\cos\left(\tfrac{1}{3}t^{3}\right)\mathrm{d}t}}$	AiryAi(z)=(exp(-(2)/(3)*(z)^((3)/(2))))/(Pi)*int(exp(- (z)^((1)/(2))* (t)^(2))*cos((1)/(3)*(t)^(3)), t = 0..infinity)	AiryAi[z]=Divide[Exp[-Divide[2,3]*(z)^(Divide[3,2])],Pi]*Integrate[Exp[- (z)^(Divide[1,2])* (t)^(2)]*Cos[Divide[1,3]*(t)^(3)], {t, 0, Infinity}]	Failure	Failure	Skip	Skip
9.5.E8	${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{e^{-\zeta}\zeta^{\ifrac{-1}{6}}}{\sqrt{\pi}(48)^{\ifrac{1}{6}}\Gamma\left(\frac{5}{6}\right)}\int_{0}^{\infty}e^{-t}t^{-\ifrac{1}{6}}\left(2+\frac{t}{\zeta}\right)^{-\ifrac{1}{6}}\mathrm{d}t}}$	AiryAi(z)=(exp(-(2)/(3)*(z)^((3)/(2)))*(2)/(3)*((z)^((3)/(2)))^((- 1)/(6)))/(sqrt(Pi)*(48)^((1)/(6))* GAMMA((5)/(6)))*int(exp(- t)*(t)^(-(1)/(6))*(2 +(t)/((2)/(3)*(z)^((3)/(2))))^(-(1)/(6)), t = 0..infinity)	AiryAi[z]=Divide[Exp[-Divide[2,3]*(z)^(Divide[3,2])]*Divide[2,3]*((z)^(Divide[3,2]))^(Divide[- 1,6]),Sqrt[Pi]*(48)^(Divide[1,6])* Gamma[Divide[5,6]]]*Integrate[Exp[- t]*(t)^(-Divide[1,6])*(2 +Divide[t,Divide[2,3]*(z)^(Divide[3,2])])^(-Divide[1,6]), {t, 0, Infinity}]	Failure	Failure	Skip	Fail Complex[-0.014252654553766713, -0.04024893384084034] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-0.014252654553766713, 0.04024893384084034] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
9.6.E2	${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\pi^{-1}\sqrt{z/3}K_{+1/3}\left(\zeta\right)}}$	AiryAi(z)= (Pi)^(- 1)*sqrt(z/ 3)*BesselK(+ 1/ 3, (2)/(3)*(z)^((3)/(2)))	AiryAi[z]= (Pi)^(- 1)*Sqrt[z/ 3]*BesselK[+ 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]	Failure	Failure	Fail 2.833765278-.3039461853*I <- {z = -2^(1/2)-I*2^(1/2)} 2.833765278+.3039461853*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[2.8337652800788264, -0.3039461861802381] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[2.8337652800788264, 0.3039461861802381] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E2	${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\pi^{-1}\sqrt{z/3}K_{-1/3}\left(\zeta\right)}}$	AiryAi(z)= (Pi)^(- 1)*sqrt(z/ 3)*BesselK(- 1/ 3, (2)/(3)*(z)^((3)/(2)))	AiryAi[z]= (Pi)^(- 1)*Sqrt[z/ 3]*BesselK[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]	Failure	Failure	Fail 2.833765278-.3039461853*I <- {z = -2^(1/2)-I*2^(1/2)} 2.833765278+.3039461853*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[2.8337652800788264, -0.3039461861802381] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[2.8337652800788264, 0.3039461861802381] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E2	${\displaystyle{\displaystyle\pi^{-1}\sqrt{z/3}K_{+1/3}\left(\zeta\right)=\tfrac{1}{3}\sqrt{z}\left(I_{-1/3}\left(\zeta\right)-I_{1/3}\left(\zeta\right)\right)}}$	(Pi)^(- 1)*sqrt(z/ 3)*BesselK(+ 1/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(3)*sqrt(z)*(BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2)))- BesselI(1/ 3, (2)/(3)*(z)^((3)/(2))))	(Pi)^(- 1)*Sqrt[z/ 3]*BesselK[+ 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,3]*Sqrt[z]*(BesselI[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselI[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Successful	Successful	-	-
9.6.E2	${\displaystyle{\displaystyle\pi^{-1}\sqrt{z/3}K_{-1/3}\left(\zeta\right)=\tfrac{1}{3}\sqrt{z}\left(I_{-1/3}\left(\zeta\right)-I_{1/3}\left(\zeta\right)\right)}}$	(Pi)^(- 1)*sqrt(z/ 3)*BesselK(- 1/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(3)*sqrt(z)*(BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2)))- BesselI(1/ 3, (2)/(3)*(z)^((3)/(2))))	(Pi)^(- 1)*Sqrt[z/ 3]*BesselK[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,3]*Sqrt[z]*(BesselI[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselI[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Successful	Successful	-	-
9.6.E2	${\displaystyle{\displaystyle\tfrac{1}{3}\sqrt{z}\left(I_{-1/3}\left(\zeta\right)-I_{1/3}\left(\zeta\right)\right)=\tfrac{1}{2}\sqrt{z/3}e^{2\pi i/3}{H^{(1)}_{1/3}}\left(\zeta e^{\pi i/2}\right)}}$	(1)/(3)*sqrt(z)*(BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2)))- BesselI(1/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*sqrt(z/ 3)*exp(2*Pi*I/ 3)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))	Divide[1,3]*Sqrt[z]*(BesselI[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselI[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*Sqrt[z/ 3]*Exp[2*Pi*I/ 3]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]	Failure	Failure	Skip	Fail Complex[-2.8337652800788247, 0.30394618618023783] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
9.6.E2	${\displaystyle{\displaystyle\tfrac{1}{2}\sqrt{z/3}e^{2\pi i/3}{H^{(1)}_{1/3}}\left(\zeta e^{\pi i/2}\right)=\tfrac{1}{2}\sqrt{z/3}e^{\pi i/3}{H^{(1)}_{-1/3}}\left(\zeta e^{\pi i/2}\right)}}$	(1)/(2)*sqrt(z/ 3)*exp(2*Pi*I/ 3)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))=(1)/(2)*sqrt(z/ 3)*exp(Pi*I/ 3)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))	Divide[1,2]*Sqrt[z/ 3]*Exp[2*Pi*I/ 3]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]=Divide[1,2]*Sqrt[z/ 3]*Exp[Pi*I/ 3]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]	Successful	Failure	-	Successful
9.6.E2	${\displaystyle{\displaystyle\tfrac{1}{2}\sqrt{z/3}e^{\pi i/3}{H^{(1)}_{-1/3}}\left(\zeta e^{\pi i/2}\right)=\tfrac{1}{2}\sqrt{z/3}e^{-2\pi i/3}{H^{(2)}_{1/3}}\left(\zeta e^{-\pi i/2}\right)}}$	(1)/(2)*sqrt(z/ 3)*exp(Pi*I/ 3)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))=(1)/(2)*sqrt(z/ 3)*exp(- 2*Pi*I/ 3)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))	Divide[1,2]*Sqrt[z/ 3]*Exp[Pi*I/ 3]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]=Divide[1,2]*Sqrt[z/ 3]*Exp[- 2*Pi*I/ 3]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]	Failure	Failure	Skip	Fail Complex[2.8337652800788256, -0.3039461861802379] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-2.8337652800788247, -0.3039461861802372] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E2	${\displaystyle{\displaystyle\tfrac{1}{2}\sqrt{z/3}e^{-2\pi i/3}{H^{(2)}_{1/3}}\left(\zeta e^{-\pi i/2}\right)=\tfrac{1}{2}\sqrt{z/3}e^{-\pi i/3}{H^{(2)}_{-1/3}}\left(\zeta e^{-\pi i/2}\right)}}$	(1)/(2)*sqrt(z/ 3)*exp(- 2*Pi*I/ 3)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))=(1)/(2)*sqrt(z/ 3)*exp(- Pi*I/ 3)*HankelH2(- 1/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))	Divide[1,2]*Sqrt[z/ 3]*Exp[- 2*Pi*I/ 3]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]=Divide[1,2]*Sqrt[z/ 3]*Exp[- Pi*I/ 3]*HankelH2[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]	Successful	Failure	-	Successful
9.6.E3	${\displaystyle{\displaystyle\mathrm{Ai}'\left(z\right)=-\pi^{-1}(z/\sqrt{3})K_{+2/3}\left(\zeta\right)}}$	subs( temp=z, diff( AiryAi(temp), temp$(1) ) )= - (Pi)^(- 1)*(z/sqrt(3))* BesselK(+ 2/ 3, (2)/(3)*(z)^((3)/(2)))	(D[AiryAi[temp], {temp, 1}]/.temp-> z)= - (Pi)^(- 1)*(z/Sqrt[3])* BesselK[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]	Failure	Failure	Fail -.7883076520+3.485863958*I <- {z = -2^(1/2)-I*2^(1/2)} -.7883076520-3.485863958*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-0.7883076520663912, 3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-0.7883076520663912, -3.485863960601928] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E3	${\displaystyle{\displaystyle\mathrm{Ai}'\left(z\right)=-\pi^{-1}(z/\sqrt{3})K_{-2/3}\left(\zeta\right)}}$	subs( temp=z, diff( AiryAi(temp), temp$(1) ) )= - (Pi)^(- 1)*(z/sqrt(3))* BesselK(- 2/ 3, (2)/(3)*(z)^((3)/(2)))	(D[AiryAi[temp], {temp, 1}]/.temp-> z)= - (Pi)^(- 1)*(z/Sqrt[3])* BesselK[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]	Failure	Failure	Fail -.7883076520+3.485863958*I <- {z = -2^(1/2)-I*2^(1/2)} -.7883076520-3.485863958*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-0.7883076520663912, 3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-0.7883076520663912, -3.485863960601928] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E3	${\displaystyle{\displaystyle-\pi^{-1}(z/\sqrt{3})K_{+2/3}\left(\zeta\right)=(z/3)\left(I_{2/3}\left(\zeta\right)-I_{-2/3}\left(\zeta\right)\right)}}$	- (Pi)^(- 1)*(z/sqrt(3))* BesselK(+ 2/ 3, (2)/(3)*(z)^((3)/(2)))=(z/ 3)*(BesselI(2/ 3, (2)/(3)*(z)^((3)/(2)))- BesselI(- 2/ 3, (2)/(3)*(z)^((3)/(2))))	- (Pi)^(- 1)*(z/Sqrt[3])* BesselK[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]=(z/ 3)*(BesselI[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselI[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Successful	Successful	-	-
9.6.E3	${\displaystyle{\displaystyle-\pi^{-1}(z/\sqrt{3})K_{-2/3}\left(\zeta\right)=(z/3)\left(I_{2/3}\left(\zeta\right)-I_{-2/3}\left(\zeta\right)\right)}}$	- (Pi)^(- 1)*(z/sqrt(3))* BesselK(- 2/ 3, (2)/(3)*(z)^((3)/(2)))=(z/ 3)*(BesselI(2/ 3, (2)/(3)*(z)^((3)/(2)))- BesselI(- 2/ 3, (2)/(3)*(z)^((3)/(2))))	- (Pi)^(- 1)*(z/Sqrt[3])* BesselK[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]=(z/ 3)*(BesselI[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselI[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Successful	Successful	-	-
9.6.E3	${\displaystyle{\displaystyle(z/3)\left(I_{2/3}\left(\zeta\right)-I_{-2/3}\left(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})e^{-\pi i/6}{H^{(1)}_{2/3}}\left(\zeta e^{\pi i/2}\right)}}$	(z/ 3)*(BesselI(2/ 3, (2)/(3)*(z)^((3)/(2)))- BesselI(- 2/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*(z/sqrt(3))* exp(- Pi*I/ 6)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))	(z/ 3)*(BesselI[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselI[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*(z/Sqrt[3])* Exp[- Pi*I/ 6]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]	Failure	Failure	Skip	Fail Complex[0.7883076520663918, -3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
9.6.E3	${\displaystyle{\displaystyle\tfrac{1}{2}(z/\sqrt{3})e^{-\pi i/6}{H^{(1)}_{2/3}}\left(\zeta e^{\pi i/2}\right)=\tfrac{1}{2}(z/\sqrt{3})e^{-5\pi i/6}{H^{(1)}_{-2/3}}\left(\zeta e^{\pi i/2}\right)}}$	(1)/(2)*(z/sqrt(3))* exp(- Pi*I/ 6)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))=(1)/(2)*(z/sqrt(3))* exp(- 5*Pi*I/ 6)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))	Divide[1,2]*(z/Sqrt[3])* Exp[- Pi*I/ 6]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]=Divide[1,2]*(z/Sqrt[3])* Exp[- 5*Pi*I/ 6]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]	Successful	Failure	-	Successful
9.6.E3	${\displaystyle{\displaystyle\tfrac{1}{2}(z/\sqrt{3})e^{-5\pi i/6}{H^{(1)}_{-2/3}}\left(\zeta e^{\pi i/2}\right)=\tfrac{1}{2}(z/\sqrt{3})e^{\pi i/6}{H^{(2)}_{2/3}}\left(\zeta e^{-\pi i/2}\right)}}$	(1)/(2)*(z/sqrt(3))* exp(- 5*Pi*I/ 6)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2))=(1)/(2)*(z/sqrt(3))* exp(Pi*I/ 6)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))	Divide[1,2]*(z/Sqrt[3])* Exp[- 5*Pi*I/ 6]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]]=Divide[1,2]*(z/Sqrt[3])* Exp[Pi*I/ 6]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]	Failure	Failure	Skip	Fail Complex[-0.7883076520663909, 3.485863960601928] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.7883076520663926, 3.485863960601928] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E3	${\displaystyle{\displaystyle\tfrac{1}{2}(z/\sqrt{3})e^{\pi i/6}{H^{(2)}_{2/3}}\left(\zeta e^{-\pi i/2}\right)=\tfrac{1}{2}(z/\sqrt{3})e^{5\pi i/6}{H^{(2)}_{-2/3}}\left(\zeta e^{-\pi i/2}\right)}}$	(1)/(2)*(z/sqrt(3))* exp(Pi*I/ 6)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))=(1)/(2)*(z/sqrt(3))* exp(5*Pi*I/ 6)*HankelH2(- 2/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))	Divide[1,2]*(z/Sqrt[3])* Exp[Pi*I/ 6]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]=Divide[1,2]*(z/Sqrt[3])* Exp[5*Pi*I/ 6]*HankelH2[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]	Successful	Failure	-	Successful
9.6.E4	${\displaystyle{\displaystyle\mathrm{Bi}\left(z\right)=\sqrt{z/3}\left(I_{1/3}\left(\zeta\right)+I_{-1/3}\left(\zeta\right)\right)}}$	AiryBi(z)=sqrt(z/ 3)*(BesselI(1/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2))))	AiryBi[z]=Sqrt[z/ 3]*(BesselI[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselI[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Failure	Failure	Fail .323091265e-1+.116725832*I <- {z = -2^(1/2)-I*2^(1/2)} .323091265e-1-.116725832*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[0.032309126109843156, 0.11672583064563491] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.032309126109843156, -0.11672583064563491] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E4	${\displaystyle{\displaystyle\sqrt{z/3}\left(I_{1/3}\left(\zeta\right)+I_{-1/3}\left(\zeta\right)\right)=\tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/6}{H^{(1)}_{1/3}}\left(\zeta e^{-\pi i/2}\right)+e^{-\pi i/6}{H^{(2)}_{1/3}}\left(\zeta e^{\pi i/2}\right)\right)}}$	sqrt(z/ 3)*(BesselI(1/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*sqrt(z/ 3)*(exp(Pi*I/ 6)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))+ exp(- Pi*I/ 6)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2)))	Sqrt[z/ 3]*(BesselI[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselI[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*Sqrt[z/ 3]*(Exp[Pi*I/ 6]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]+ Exp[- Pi*I/ 6]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]])	Failure	Failure	Fail -.1681276560-1.475245556*I <- {z = -2^(1/2)-I*2^(1/2)} -.1681276560+1.475245556*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-0.16812765614504083, -1.4752455553622306] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-0.16812765614504083, 1.4752455553622306] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E4	${\displaystyle{\displaystyle\tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/6}{H^{(1)}_{1/3}}\left(\zeta e^{-\pi i/2}\right)+e^{-\pi i/6}{H^{(2)}_{1/3}}\left(\zeta e^{\pi i/2}\right)\right)=\tfrac{1}{2}\sqrt{z/3}\left(e^{-\pi i/6}{H^{(1)}_{-1/3}}\left(\zeta e^{-\pi i/2}\right)+e^{\pi i/6}{H^{(2)}_{-1/3}}\left(\zeta e^{\pi i/2}\right)\right)}}$	(1)/(2)*sqrt(z/ 3)*(exp(Pi*I/ 6)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))+ exp(- Pi*I/ 6)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2)))=(1)/(2)*sqrt(z/ 3)*(exp(- Pi*I/ 6)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))+ exp(Pi*I/ 6)*HankelH2(- 1/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2)))	Divide[1,2]*Sqrt[z/ 3]*(Exp[Pi*I/ 6]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]+ Exp[- Pi*I/ 6]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]])=Divide[1,2]*Sqrt[z/ 3]*(Exp[- Pi*I/ 6]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]+ Exp[Pi*I/ 6]*HankelH2[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]])	Successful	Failure	-	Successful
9.6.E5	${\displaystyle{\displaystyle\mathrm{Bi}'\left(z\right)=(z/\sqrt{3})\left(I_{2/3}\left(\zeta\right)+I_{-2/3}\left(\zeta\right)\right)}}$	subs( temp=z, diff( AiryBi(temp), temp$(1) ) )=(z/sqrt(3))*(BesselI(2/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselI(- 2/ 3, (2)/(3)*(z)^((3)/(2))))	(D[AiryBi[temp], {temp, 1}]/.temp-> z)=(z/Sqrt[3])*(BesselI[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselI[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Failure	Failure	Fail .181539689+.267445042e-1*I <- {z = -2^(1/2)-I*2^(1/2)} .181539689-.267445042e-1*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[0.18153969005752768, 0.026744504839266825] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.18153969005752768, -0.026744504839266825] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E5	${\displaystyle{\displaystyle(z/\sqrt{3})\left(I_{2/3}\left(\zeta\right)+I_{-2/3}\left(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})\left(e^{\pi i/3}{H^{(1)}_{2/3}}\left(\zeta e^{-\pi i/2}\right)+e^{-\pi i/3}{H^{(2)}_{2/3}}\left(\zeta e^{\pi i/2}\right)\right)}}$	(z/sqrt(3))*(BesselI(2/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselI(- 2/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*(z/sqrt(3))*(exp(Pi*I/ 3)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))+ exp(- Pi*I/ 3)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2)))	(z/Sqrt[3])*(BesselI[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselI[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*(z/Sqrt[3])*(Exp[Pi*I/ 3]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]+ Exp[- Pi*I/ 3]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]])	Failure	Failure	Fail 1.652162135+.3807815744*I <- {z = -2^(1/2)-I*2^(1/2)} 1.652162135-.3807815744*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[1.6521621352721998, 0.3807815736135619] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[1.6521621352721998, -0.3807815736135619] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E5	${\displaystyle{\displaystyle\tfrac{1}{2}(z/\sqrt{3})\left(e^{\pi i/3}{H^{(1)}_{2/3}}\left(\zeta e^{-\pi i/2}\right)+e^{-\pi i/3}{H^{(2)}_{2/3}}\left(\zeta e^{\pi i/2}\right)\right)=\tfrac{1}{2}(z/\sqrt{3})\left(e^{-\pi i/3}{H^{(1)}_{-2/3}}\left(\zeta e^{-\pi i/2}\right)+e^{\pi i/3}{H^{(2)}_{-2/3}}\left(\zeta e^{\pi i/2}\right)\right)}}$	(1)/(2)*(z/sqrt(3))*(exp(Pi*I/ 3)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))+ exp(- Pi*I/ 3)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2)))=(1)/(2)*(z/sqrt(3))*(exp(- Pi*I/ 3)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2))*exp(- Pi*I/ 2))+ exp(Pi*I/ 3)*HankelH2(- 2/ 3, (2)/(3)*(z)^((3)/(2))*exp(Pi*I/ 2)))	Divide[1,2]*(z/Sqrt[3])*(Exp[Pi*I/ 3]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]+ Exp[- Pi*I/ 3]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]])=Divide[1,2]*(z/Sqrt[3])*(Exp[- Pi*I/ 3]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[- Pi*I/ 2]]+ Exp[Pi*I/ 3]*HankelH2[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])*Exp[Pi*I/ 2]])	Successful	Failure	-	Successful
9.6.E6	${\displaystyle{\displaystyle\mathrm{Ai}\left(-z\right)=(\sqrt{z}/3)\left(J_{1/3}\left(\zeta\right)+J_{-1/3}\left(\zeta\right)\right)}}$	AiryAi(- z)=(sqrt(z)/ 3)*(BesselJ(1/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselJ(- 1/ 3, (2)/(3)*(z)^((3)/(2))))	AiryAi[- z]=(Sqrt[z]/ 3)*(BesselJ[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselJ[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Failure	Failure	Fail -.5274645816-.7652257224e-1*I <- {z = -2^(1/2)-I*2^(1/2)} -.5274645816+.7652257224e-1*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-0.5274645818155765, -0.0765225723412053] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-0.5274645818155765, 0.0765225723412053] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E6	${\displaystyle{\displaystyle(\sqrt{z}/3)\left(J_{1/3}\left(\zeta\right)+J_{-1/3}\left(\zeta\right)\right)=\tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/6}{H^{(1)}_{1/3}}\left(\zeta\right)+e^{-\pi i/6}{H^{(2)}_{1/3}}\left(\zeta\right)\right)}}$	(sqrt(z)/ 3)*(BesselJ(1/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselJ(- 1/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*sqrt(z/ 3)*(exp(Pi*I/ 6)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- Pi*I/ 6)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))))	(Sqrt[z]/ 3)*(BesselJ[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselJ[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*Sqrt[z/ 3]*(Exp[Pi*I/ 6]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- Pi*I/ 6]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Successful	Failure	-	Successful
9.6.E6	${\displaystyle{\displaystyle\tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/6}{H^{(1)}_{1/3}}\left(\zeta\right)+e^{-\pi i/6}{H^{(2)}_{1/3}}\left(\zeta\right)\right)=\tfrac{1}{2}\sqrt{z/3}\left(e^{-\pi i/6}{H^{(1)}_{-1/3}}\left(\zeta\right)+e^{\pi i/6}{H^{(2)}_{-1/3}}\left(\zeta\right)\right)}}$	(1)/(2)*sqrt(z/ 3)*(exp(Pi*I/ 6)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- Pi*I/ 6)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*sqrt(z/ 3)*(exp(- Pi*I/ 6)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(Pi*I/ 6)*HankelH2(- 1/ 3, (2)/(3)*(z)^((3)/(2))))	Divide[1,2]*Sqrt[z/ 3]*(Exp[Pi*I/ 6]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- Pi*I/ 6]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*Sqrt[z/ 3]*(Exp[- Pi*I/ 6]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[Pi*I/ 6]*HankelH2[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Successful	Successful	-	-
9.6.E7	${\displaystyle{\displaystyle\mathrm{Ai}'\left(-z\right)=(z/3)\left(J_{2/3}\left(\zeta\right)-J_{-2/3}\left(\zeta\right)\right)}}$	subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )=(z/ 3)*(BesselJ(2/ 3, (2)/(3)*(z)^((3)/(2)))- BesselJ(- 2/ 3, (2)/(3)*(z)^((3)/(2))))	(D[AiryAi[temp], {temp, 1}]/.temp-> - z)=(z/ 3)*(BesselJ[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselJ[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Failure	Failure	Fail -.6239178317-.1120108402*I <- {z = -2^(1/2)-I*2^(1/2)} -.6239178317+.1120108402*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-0.6239178317433629, -0.1120108405877985] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-0.6239178317433629, 0.1120108405877985] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E7	${\displaystyle{\displaystyle(z/3)\left(J_{2/3}\left(\zeta\right)-J_{-2/3}\left(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})\left(e^{-\pi i/6}{H^{(1)}_{2/3}}\left(\zeta\right)+e^{\pi i/6}{H^{(2)}_{2/3}}\left(\zeta\right)\right)}}$	(z/ 3)*(BesselJ(2/ 3, (2)/(3)*(z)^((3)/(2)))- BesselJ(- 2/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*(z/sqrt(3))*(exp(- Pi*I/ 6)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(Pi*I/ 6)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))))	(z/ 3)*(BesselJ[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselJ[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*(z/Sqrt[3])*(Exp[- Pi*I/ 6]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[Pi*I/ 6]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Successful	Failure	-	Successful
9.6.E7	${\displaystyle{\displaystyle\tfrac{1}{2}(z/\sqrt{3})\left(e^{-\pi i/6}{H^{(1)}_{2/3}}\left(\zeta\right)+e^{\pi i/6}{H^{(2)}_{2/3}}\left(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})\left(e^{-5\pi i/6}{H^{(1)}_{-2/3}}\left(\zeta\right)+e^{5\pi i/6}{H^{(2)}_{-2/3}}\left(\zeta\right)\right)}}$	(1)/(2)*(z/sqrt(3))*(exp(- Pi*I/ 6)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(Pi*I/ 6)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*(z/sqrt(3))*(exp(- 5*Pi*I/ 6)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(5*Pi*I/ 6)*HankelH2(- 2/ 3, (2)/(3)*(z)^((3)/(2))))	Divide[1,2]*(z/Sqrt[3])*(Exp[- Pi*I/ 6]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[Pi*I/ 6]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*(z/Sqrt[3])*(Exp[- 5*Pi*I/ 6]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[5*Pi*I/ 6]*HankelH2[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Successful	Successful	-	-
9.6.E8	${\displaystyle{\displaystyle\mathrm{Bi}\left(-z\right)=\sqrt{z/3}\left(J_{-1/3}\left(\zeta\right)-J_{1/3}\left(\zeta\right)\right)}}$	AiryBi(- z)=sqrt(z/ 3)*(BesselJ(- 1/ 3, (2)/(3)*(z)^((3)/(2)))- BesselJ(1/ 3, (2)/(3)*(z)^((3)/(2))))	AiryBi[- z]=Sqrt[z/ 3]*(BesselJ[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselJ[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Failure	Failure	Fail .4111747943+1.355498750*I <- {z = -2^(1/2)-I*2^(1/2)} .4111747943-1.355498750*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[0.41117479327057227, 1.355498750084894] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.41117479327057227, -1.355498750084894] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E8	${\displaystyle{\displaystyle\sqrt{z/3}\left(J_{-1/3}\left(\zeta\right)-J_{1/3}\left(\zeta\right)\right)=\tfrac{1}{2}\sqrt{z/3}\left(e^{2\pi i/3}{H^{(1)}_{1/3}}\left(\zeta\right)+e^{-2\pi i/3}{H^{(2)}_{1/3}}\left(\zeta\right)\right)}}$	sqrt(z/ 3)*(BesselJ(- 1/ 3, (2)/(3)*(z)^((3)/(2)))- BesselJ(1/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*sqrt(z/ 3)*(exp(2*Pi*I/ 3)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- 2*Pi*I/ 3)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))))	Sqrt[z/ 3]*(BesselJ[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]- BesselJ[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*Sqrt[z/ 3]*(Exp[2*Pi*I/ 3]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- 2*Pi*I/ 3]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Successful	Failure	-	Successful
9.6.E8	${\displaystyle{\displaystyle\tfrac{1}{2}\sqrt{z/3}\left(e^{2\pi i/3}{H^{(1)}_{1/3}}\left(\zeta\right)+e^{-2\pi i/3}{H^{(2)}_{1/3}}\left(\zeta\right)\right)=\tfrac{1}{2}\sqrt{z/3}\left(e^{\pi i/3}{H^{(1)}_{-1/3}}\left(\zeta\right)+e^{-\pi i/3}{H^{(2)}_{-1/3}}\left(\zeta\right)\right)}}$	(1)/(2)*sqrt(z/ 3)*(exp(2*Pi*I/ 3)*HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- 2*Pi*I/ 3)*HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*sqrt(z/ 3)*(exp(Pi*I/ 3)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- Pi*I/ 3)*HankelH2(- 1/ 3, (2)/(3)*(z)^((3)/(2))))	Divide[1,2]*Sqrt[z/ 3]*(Exp[2*Pi*I/ 3]*HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- 2*Pi*I/ 3]*HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*Sqrt[z/ 3]*(Exp[Pi*I/ 3]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- Pi*I/ 3]*HankelH2[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Successful	Successful	-	-
9.6.E9	${\displaystyle{\displaystyle\mathrm{Bi}'\left(-z\right)=(z/\sqrt{3})\left(J_{-2/3}\left(\zeta\right)+J_{2/3}\left(\zeta\right)\right)}}$	subs( temp=- z, diff( AiryBi(temp), temp$(1) ) )=(z/sqrt(3))*(BesselJ(- 2/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselJ(2/ 3, (2)/(3)*(z)^((3)/(2))))	(D[AiryBi[temp], {temp, 1}]/.temp-> - z)=(z/Sqrt[3])*(BesselJ[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselJ[2/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Failure	Failure	Fail -1.338452844+1.884861589*I <- {z = -2^(1/2)-I*2^(1/2)} -1.338452844-1.884861589*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-1.338452844987923, 1.884861589266007] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-1.338452844987923, -1.884861589266007] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E9	${\displaystyle{\displaystyle(z/\sqrt{3})\left(J_{-2/3}\left(\zeta\right)+J_{2/3}\left(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})\left(e^{\pi i/3}{H^{(1)}_{2/3}}\left(\zeta\right)+e^{-\pi i/3}{H^{(2)}_{2/3}}\left(\zeta\right)\right)}}$	(z/sqrt(3))*(BesselJ(- 2/ 3, (2)/(3)*(z)^((3)/(2)))+ BesselJ(2/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*(z/sqrt(3))*(exp(Pi*I/ 3)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- Pi*I/ 3)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))))	(z/Sqrt[3])*(BesselJ[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ BesselJ[2/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*(z/Sqrt[3])*(Exp[Pi*I/ 3]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- Pi*I/ 3]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Successful	Failure	-	Successful
9.6.E9	${\displaystyle{\displaystyle\tfrac{1}{2}(z/\sqrt{3})\left(e^{\pi i/3}{H^{(1)}_{2/3}}\left(\zeta\right)+e^{-\pi i/3}{H^{(2)}_{2/3}}\left(\zeta\right)\right)=\tfrac{1}{2}(z/\sqrt{3})\left(e^{-\pi i/3}{H^{(1)}_{-2/3}}\left(\zeta\right)+e^{\pi i/3}{H^{(2)}_{-2/3}}\left(\zeta\right)\right)}}$	(1)/(2)*(z/sqrt(3))*(exp(Pi*I/ 3)*HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(- Pi*I/ 3)*HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2))))=(1)/(2)*(z/sqrt(3))*(exp(- Pi*I/ 3)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2)))+ exp(Pi*I/ 3)*HankelH2(- 2/ 3, (2)/(3)*(z)^((3)/(2))))	Divide[1,2]*(z/Sqrt[3])*(Exp[Pi*I/ 3]*HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[- Pi*I/ 3]*HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])])=Divide[1,2]*(z/Sqrt[3])*(Exp[- Pi*I/ 3]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]+ Exp[Pi*I/ 3]*HankelH2[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])])	Successful	Successful	-	-
9.6.E11	${\displaystyle{\displaystyle J_{+1/3}\left(\zeta\right)=\tfrac{1}{2}\sqrt{3/z}\left(\sqrt{3}\mathrm{Ai}\left(-z\right)-\mathrm{Bi}\left(-z\right)\right)}}$	BesselJ(+ 1/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*sqrt(3/ z)*(sqrt(3)*AiryAi(- z)- AiryBi(- z))	BesselJ[+ 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*Sqrt[3/ z]*(Sqrt[3]*AiryAi[- z]- AiryBi[- z])	Failure	Failure	Fail -.5314179186+1.098214195*I <- {z = -2^(1/2)-I*2^(1/2)} -.5314179186-1.098214195*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-0.531417918807772, 1.09821419470116] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-0.531417918807772, -1.09821419470116] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E11	${\displaystyle{\displaystyle J_{-1/3}\left(\zeta\right)=\tfrac{1}{2}\sqrt{3/z}\left(\sqrt{3}\mathrm{Ai}\left(-z\right)+\mathrm{Bi}\left(-z\right)\right)}}$	BesselJ(- 1/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*sqrt(3/ z)*(sqrt(3)*AiryAi(- z)+ AiryBi(- z))	BesselJ[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*Sqrt[3/ z]*(Sqrt[3]*AiryAi[- z]+ AiryBi[- z])	Failure	Failure	Fail .8096382420-.23450870e-2*I <- {z = -2^(1/2)-I*2^(1/2)} .8096382420+.23450870e-2*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[0.8096382422763857, -0.0023450862884800416] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.8096382422763857, 0.0023450862884800416] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E12	${\displaystyle{\displaystyle J_{+2/3}\left(\zeta\right)=\tfrac{1}{2}(\sqrt{3}/z)\left(+\sqrt{3}\mathrm{Ai}'\left(-z\right)+\mathrm{Bi}'\left(-z\right)\right)}}$	BesselJ(+ 2/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*(sqrt(3)/ z)*(+sqrt(3)*subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )+ subs( temp=- z, diff( AiryBi(temp), temp$(1) ) ))	BesselJ[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*(Sqrt[3]/ z)*(+Sqrt[3]*(D[AiryAi[temp], {temp, 1}]/.temp-> - z)+ (D[AiryBi[temp], {temp, 1}]/.temp-> - z))	Failure	Failure	Fail -.2229822889+1.258414134*I <- {z = -2^(1/2)-I*2^(1/2)} -.2229822889-1.258414134*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-0.22298228919670726, 1.2584141341459216] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-0.22298228919670726, -1.2584141341459216] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E12	${\displaystyle{\displaystyle J_{-2/3}\left(\zeta\right)=\tfrac{1}{2}(\sqrt{3}/z)\left(-\sqrt{3}\mathrm{Ai}'\left(-z\right)+\mathrm{Bi}'\left(-z\right)\right)}}$	BesselJ(- 2/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*(sqrt(3)/ z)*(-sqrt(3)*subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )+ subs( temp=- z, diff( AiryBi(temp), temp$(1) ) ))	BesselJ[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*(Sqrt[3]/ z)*(-Sqrt[3]*(D[AiryAi[temp], {temp, 1}]/.temp-> - z)+ (D[AiryBi[temp], {temp, 1}]/.temp-> - z))	Failure	Failure	Fail .5575879430+.7154547765*I <- {z = -2^(1/2)-I*2^(1/2)} .5575879430-.7154547765*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[0.5575879428157583, 0.7154547769715692] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.5575879428157583, -0.7154547769715692] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E13	${\displaystyle{\displaystyle I_{+1/3}\left(\zeta\right)=\tfrac{1}{2}\sqrt{3/z}\left(-\sqrt{3}\mathrm{Ai}\left(z\right)+\mathrm{Bi}\left(z\right)\right)}}$	BesselI(+ 1/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*sqrt(3/ z)*(-sqrt(3)*AiryAi(z)+ AiryBi(z))	BesselI[+ 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*Sqrt[3/ z]*(-Sqrt[3]*AiryAi[z]+ AiryBi[z])	Failure	Failure	Fail 1.506527799+2.607865458*I <- {z = -2^(1/2)-I*2^(1/2)} 1.506527799-2.607865458*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[1.5065278006053275, 2.6078654586738588] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[1.5065278006053275, -2.6078654586738588] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E13	${\displaystyle{\displaystyle I_{-1/3}\left(\zeta\right)=\tfrac{1}{2}\sqrt{3/z}\left(+\sqrt{3}\mathrm{Ai}\left(z\right)+\mathrm{Bi}\left(z\right)\right)}}$	BesselI(- 1/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*sqrt(3/ z)*(+sqrt(3)*AiryAi(z)+ AiryBi(z))	BesselI[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*Sqrt[3/ z]*(+Sqrt[3]*AiryAi[z]+ AiryBi[z])	Failure	Failure	Fail -1.389593520-2.699131954*I <- {z = -2^(1/2)-I*2^(1/2)} -1.389593520+2.699131954*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-1.3895935221249858, -2.6991319545588484] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-1.3895935221249858, 2.6991319545588484] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E14	${\displaystyle{\displaystyle I_{+2/3}\left(\zeta\right)=\tfrac{1}{2}(\sqrt{3}/z)\left(+\sqrt{3}\mathrm{Ai}'\left(z\right)+\mathrm{Bi}'\left(z\right)\right)}}$	BesselI(+ 2/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*(sqrt(3)/ z)*(+sqrt(3)*subs( temp=z, diff( AiryAi(temp), temp$(1) ) )+ subs( temp=z, diff( AiryBi(temp), temp$(1) ) ))	BesselI[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*(Sqrt[3]/ z)*(+Sqrt[3]*(D[AiryAi[temp], {temp, 1}]/.temp-> z)+ (D[AiryBi[temp], {temp, 1}]/.temp-> z))	Failure	Failure	Fail 1.494369018+2.219325646*I <- {z = -2^(1/2)-I*2^(1/2)} 1.494369018-2.219325646*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[1.4943690186714658, 2.219325646151564] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[1.4943690186714658, -2.219325646151564] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E14	${\displaystyle{\displaystyle I_{-2/3}\left(\zeta\right)=\tfrac{1}{2}(\sqrt{3}/z)\left(-\sqrt{3}\mathrm{Ai}'\left(z\right)+\mathrm{Bi}'\left(z\right)\right)}}$	BesselI(- 2/ 3, (2)/(3)*(z)^((3)/(2)))=(1)/(2)*(sqrt(3)/ z)*(-sqrt(3)*subs( temp=z, diff( AiryAi(temp), temp$(1) ) )+ subs( temp=z, diff( AiryBi(temp), temp$(1) ) ))	BesselI[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]=Divide[1,2]*(Sqrt[3]/ z)*(-Sqrt[3]*(D[AiryAi[temp], {temp, 1}]/.temp-> z)+ (D[AiryBi[temp], {temp, 1}]/.temp-> z))	Failure	Failure	Fail -1.366821518-2.314117950*I <- {z = -2^(1/2)-I*2^(1/2)} -1.366821518+2.314117950*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-1.366821518925578, -2.3141179507576517] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-1.366821518925578, 2.3141179507576517] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E15	${\displaystyle{\displaystyle K_{+1/3}\left(\zeta\right)=\pi\sqrt{3/z}\mathrm{Ai}\left(z\right)}}$	BesselK(+ 1/ 3, (2)/(3)*(z)^((3)/(2)))= Pi*sqrt(3/ z)*AiryAi(z)	BesselK[+ 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Pi*Sqrt[3/ z]*AiryAi[z]	Failure	Failure	Fail -5.252983010-9.625828533*I <- {z = -2^(1/2)-I*2^(1/2)} -5.252983010+9.625828533*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-5.252983013913404, -9.625828534114124] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.252983013913404, 9.625828534114124] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E15	${\displaystyle{\displaystyle K_{-1/3}\left(\zeta\right)=\pi\sqrt{3/z}\mathrm{Ai}\left(z\right)}}$	BesselK(- 1/ 3, (2)/(3)*(z)^((3)/(2)))= Pi*sqrt(3/ z)*AiryAi(z)	BesselK[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Pi*Sqrt[3/ z]*AiryAi[z]	Failure	Failure	Fail -5.252983010-9.625828533*I <- {z = -2^(1/2)-I*2^(1/2)} -5.252983010+9.625828533*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-5.252983013913404, -9.625828534114124] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.252983013913404, 9.625828534114124] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E16	${\displaystyle{\displaystyle K_{+2/3}\left(\zeta\right)=-\pi(\sqrt{3}/z)\mathrm{Ai}'\left(z\right)}}$	BesselK(+ 2/ 3, (2)/(3)*(z)^((3)/(2)))= - Pi*(sqrt(3)/ z)* subs( temp=z, diff( AiryAi(temp), temp$(1) ) )	BesselK[+ 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]= - Pi*(Sqrt[3]/ z)* (D[AiryAi[temp], {temp, 1}]/.temp-> z)	Failure	Failure	Fail -5.189625577-8.222757114*I <- {z = -2^(1/2)-I*2^(1/2)} -5.189625577+8.222757114*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-5.189625578046477, -8.222757113865619] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.189625578046477, 8.222757113865619] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E16	${\displaystyle{\displaystyle K_{-2/3}\left(\zeta\right)=-\pi(\sqrt{3}/z)\mathrm{Ai}'\left(z\right)}}$	BesselK(- 2/ 3, (2)/(3)*(z)^((3)/(2)))= - Pi*(sqrt(3)/ z)* subs( temp=z, diff( AiryAi(temp), temp$(1) ) )	BesselK[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]= - Pi*(Sqrt[3]/ z)* (D[AiryAi[temp], {temp, 1}]/.temp-> z)	Failure	Failure	Fail -5.189625577-8.222757114*I <- {z = -2^(1/2)-I*2^(1/2)} -5.189625577+8.222757114*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-5.189625578046477, -8.222757113865619] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-5.189625578046477, 8.222757113865619] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E17	${\displaystyle{\displaystyle{H^{(1)}_{1/3}}\left(\zeta\right)=e^{-\pi i/3}{H^{(1)}_{-1/3}}\left(\zeta\right)}}$	HankelH1(1/ 3, (2)/(3)*(z)^((3)/(2)))= exp(- Pi*I/ 3)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2)))	HankelH1[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[- Pi*I/ 3]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]	Successful	Successful	-	-
9.6.E17	${\displaystyle{\displaystyle e^{-\pi i/3}{H^{(1)}_{-1/3}}\left(\zeta\right)=e^{-\pi i/6}\sqrt{3/z}\left(\mathrm{Ai}\left(-z\right)-i\mathrm{Bi}\left(-z\right)\right)}}$	exp(- Pi*I/ 3)*HankelH1(- 1/ 3, (2)/(3)*(z)^((3)/(2)))= exp(- Pi*I/ 6)*sqrt(3/ z)*(AiryAi(- z)- I*AiryBi(- z))	Exp[- Pi*I/ 3]*HankelH1[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[- Pi*I/ 6]*Sqrt[3/ z]*(AiryAi[- z]- I*AiryBi[- z])	Failure	Failure	Fail -1.168180054-.1434897976*I <- {z = -2^(1/2)-I*2^(1/2)} .1053442159-2.339918189*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-1.1681800521462087, -0.14348979802367162] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.10534421453066467, -2.3399181874259916] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E18	${\displaystyle{\displaystyle{H^{(1)}_{2/3}}\left(\zeta\right)=e^{-2\pi i/3}{H^{(1)}_{-2/3}}\left(\zeta\right)}}$	HankelH1(2/ 3, (2)/(3)*(z)^((3)/(2)))= exp(- 2*Pi*I/ 3)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2)))	HankelH1[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[- 2*Pi*I/ 3]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]	Successful	Successful	-	-
9.6.E18	${\displaystyle{\displaystyle e^{-2\pi i/3}{H^{(1)}_{-2/3}}\left(\zeta\right)=e^{\pi i/6}(\sqrt{3}/z)\left(\mathrm{Ai}'\left(-z\right)-i\mathrm{Bi}'\left(-z\right)\right)}}$	exp(- 2*Pi*I/ 3)*HankelH1(- 2/ 3, (2)/(3)*(z)^((3)/(2)))= exp(Pi*I/ 6)*(sqrt(3)/ z)*(subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )- I*subs( temp=- z, diff( AiryBi(temp), temp$(1) ) ))	Exp[- 2*Pi*I/ 3]*HankelH1[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[Pi*I/ 6]*(Sqrt[3]/ z)*((D[AiryAi[temp], {temp, 1}]/.temp-> - z)- I*(D[AiryBi[temp], {temp, 1}]/.temp-> - z))	Failure	Failure	Fail 1.329699466+.7433059206*I <- {z = -2^(1/2)-I*2^(1/2)} -1.775664044-1.773522348*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[1.3296994660595483, 0.7433059210750237] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-1.775664044452963, -1.7735223472168191] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E19	${\displaystyle{\displaystyle{H^{(2)}_{1/3}}\left(\zeta\right)=e^{\pi i/3}{H^{(2)}_{-1/3}}\left(\zeta\right)}}$	HankelH2(1/ 3, (2)/(3)*(z)^((3)/(2)))= exp(Pi*I/ 3)*HankelH2(- 1/ 3, (2)/(3)*(z)^((3)/(2)))	HankelH2[1/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[Pi*I/ 3]*HankelH2[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]	Successful	Successful	-	-
9.6.E19	${\displaystyle{\displaystyle e^{\pi i/3}{H^{(2)}_{-1/3}}\left(\zeta\right)=e^{\pi i/6}\sqrt{3/z}\left(\mathrm{Ai}\left(-z\right)+i\mathrm{Bi}\left(-z\right)\right)}}$	exp(Pi*I/ 3)*HankelH2(- 1/ 3, (2)/(3)*(z)^((3)/(2)))= exp(Pi*I/ 6)*sqrt(3/ z)*(AiryAi(- z)+ I*AiryBi(- z))	Exp[Pi*I/ 3]*HankelH2[- 1/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[Pi*I/ 6]*Sqrt[3/ z]*(AiryAi[- z]+ I*AiryBi[- z])	Failure	Failure	Fail .1053442159+2.339918189*I <- {z = -2^(1/2)-I*2^(1/2)} -1.168180054+.1434897976*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[0.10534421453066467, 2.3399181874259916] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-1.1681800521462087, 0.14348979802367162] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E20	${\displaystyle{\displaystyle{H^{(2)}_{2/3}}\left(\zeta\right)=e^{2\pi i/3}{H^{(2)}_{-2/3}}\left(\zeta\right)}}$	HankelH2(2/ 3, (2)/(3)*(z)^((3)/(2)))= exp(2*Pi*I/ 3)*HankelH2(- 2/ 3, (2)/(3)*(z)^((3)/(2)))	HankelH2[2/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[2*Pi*I/ 3]*HankelH2[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]	Successful	Successful	-	-
9.6.E20	${\displaystyle{\displaystyle e^{2\pi i/3}{H^{(2)}_{-2/3}}\left(\zeta\right)=e^{-\pi i/6}(\sqrt{3}/z)\left(\mathrm{Ai}'\left(-z\right)+i\mathrm{Bi}'\left(-z\right)\right)}}$	exp(2*Pi*I/ 3)*HankelH2(- 2/ 3, (2)/(3)*(z)^((3)/(2)))= exp(- Pi*I/ 6)*(sqrt(3)/ z)*(subs( temp=- z, diff( AiryAi(temp), temp$(1) ) )+ I*subs( temp=- z, diff( AiryBi(temp), temp$(1) ) ))	Exp[2*Pi*I/ 3]*HankelH2[- 2/ 3, Divide[2,3]*(z)^(Divide[3,2])]= Exp[- Pi*I/ 6]*(Sqrt[3]/ z)*((D[AiryAi[temp], {temp, 1}]/.temp-> - z)+ I*(D[AiryBi[temp], {temp, 1}]/.temp-> - z))	Failure	Failure	Fail -1.775664044+1.773522348*I <- {z = -2^(1/2)-I*2^(1/2)} 1.329699466-.7433059206*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-1.775664044452963, 1.7735223472168191] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[1.3296994660595483, -0.7433059210750237] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E22	${\displaystyle{\displaystyle\mathrm{Ai}'\left(z\right)=-\tfrac{1}{2}\pi^{-1/2}z^{1/4}W_{0,2/3}\left(2\zeta\right)}}$	subs( temp=z, diff( AiryAi(temp), temp$(1) ) )= -(1)/(2)*(Pi)^(- 1/ 2)* (z)^(1/ 4)* WhittakerW(0, 2/ 3, 2*(2)/(3)*(z)^((3)/(2)))	(D[AiryAi[temp], {temp, 1}]/.temp-> z)= -Divide[1,2]*(Pi)^(- 1/ 2)* (z)^(1/ 4)* WhittakerW[0, 2/ 3, 2*Divide[2,3]*(z)^(Divide[3,2])]	Failure	Failure	Fail .89148347e-2-.60513229e-1*I <- {z = -2^(1/2)-I*2^(1/2)} .89148347e-2+.60513229e-1*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[0.008914834946421868, -0.06051323001917441] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[0.008914834946421868, 0.06051323001917441] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E22	${\displaystyle{\displaystyle-\tfrac{1}{2}\pi^{-1/2}z^{1/4}W_{0,2/3}\left(2\zeta\right)=-3^{1/6}\pi^{-1/2}\zeta^{4/3}e^{-\zeta}U\left(\tfrac{7}{6},\tfrac{7}{3},2\zeta\right)}}$	-(1)/(2)*(Pi)^(- 1/ 2)* (z)^(1/ 4)* WhittakerW(0, 2/ 3, 2*(2)/(3)*(z)^((3)/(2)))= - (3)^(1/ 6)* (Pi)^(- 1/ 2)*(2)/(3)*((z)^((3)/(2)))^(4/ 3)* exp(-(2)/(3)*(z)^((3)/(2)))*KummerU((7)/(6), (7)/(3), 2*(2)/(3)*(z)^((3)/(2)))	-Divide[1,2]*(Pi)^(- 1/ 2)* (z)^(1/ 4)* WhittakerW[0, 2/ 3, 2*Divide[2,3]*(z)^(Divide[3,2])]= - (3)^(1/ 6)* (Pi)^(- 1/ 2)*Divide[2,3]*((z)^(Divide[3,2]))^(4/ 3)* Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricU[Divide[7,6], Divide[7,3], 2*Divide[2,3]*(z)^(Divide[3,2])]	Failure	Failure	Fail -.316154866e-3-.241774161e-1*I <- {z = 2^(1/2)+I*2^(1/2)} -.316154866e-3+.241774161e-1*I <- {z = 2^(1/2)-I*2^(1/2)} 1.587390115+1.153455370*I <- {z = -2^(1/2)-I*2^(1/2)} 1.587390115-1.153455370*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-3.1615464995420756*^-4, -0.024177416299250604] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-3.1615464995420756*^-4, 0.024177416299250604] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[1.587390116444673, 1.153455375076458] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[1.587390116444673, -1.153455375076458] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E23	${\displaystyle{\displaystyle\mathrm{Bi}\left(z\right)=\frac{1}{2^{1/3}\Gamma\left(\tfrac{2}{3}\right)}z^{-1/4}M_{0,-1/3}\left(2\zeta\right)+\frac{3}{2^{5/3}\Gamma\left(\tfrac{1}{3}\right)}z^{-1/4}M_{0,1/3}\left(2\zeta\right)}}$	AiryBi(z)=(1)/((2)^(1/ 3)* GAMMA((2)/(3)))*(z)^(- 1/ 4)* WhittakerM(0, - 1/ 3, 2*(2)/(3)*(z)^((3)/(2)))+(3)/((2)^(5/ 3)* GAMMA((1)/(3)))*(z)^(- 1/ 4)* WhittakerM(0, 1/ 3, 2*(2)/(3)*(z)^((3)/(2)))	AiryBi[z]=Divide[1,(2)^(1/ 3)* Gamma[Divide[2,3]]]*(z)^(- 1/ 4)* WhittakerM[0, - 1/ 3, 2*Divide[2,3]*(z)^(Divide[3,2])]+Divide[3,(2)^(5/ 3)* Gamma[Divide[1,3]]]*(z)^(- 1/ 4)* WhittakerM[0, 1/ 3, 2*Divide[2,3]*(z)^(Divide[3,2])]	Failure	Failure	Fail -.3039461866-2.833765278*I <- {z = -2^(1/2)-I*2^(1/2)} -.3039461866+2.833765278*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-0.30394618618023905, -2.8337652800788256] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-0.30394618618023905, 2.8337652800788256] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E24	${\displaystyle{\displaystyle\mathrm{Bi}'\left(z\right)=\frac{2^{1/3}}{\Gamma\left(\tfrac{1}{3}\right)}z^{1/4}M_{0,-2/3}\left(2\zeta\right)+\frac{3}{2^{10/3}\Gamma\left(\tfrac{2}{3}\right)}z^{1/4}M_{0,2/3}\left(2\zeta\right)}}$	subs( temp=z, diff( AiryBi(temp), temp$(1) ) )=((2)^(1/ 3))/(GAMMA((1)/(3)))*(z)^(1/ 4)* WhittakerM(0, - 2/ 3, 2*(2)/(3)*(z)^((3)/(2)))+(3)/((2)^(10/ 3)* GAMMA((2)/(3)))*(z)^(1/ 4)* WhittakerM(0, 2/ 3, 2*(2)/(3)*(z)^((3)/(2)))	(D[AiryBi[temp], {temp, 1}]/.temp-> z)=Divide[(2)^(1/ 3),Gamma[Divide[1,3]]]*(z)^(1/ 4)* WhittakerM[0, - 2/ 3, 2*Divide[2,3]*(z)^(Divide[3,2])]+Divide[3,(2)^(10/ 3)* Gamma[Divide[2,3]]]*(z)^(1/ 4)* WhittakerM[0, 2/ 3, 2*Divide[2,3]*(z)^(Divide[3,2])]	Failure	Failure	Fail 3.485863958+.7883076513*I <- {z = -2^(1/2)-I*2^(1/2)} 3.485863958-.7883076513*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[3.485863960601927, 0.7883076520663903] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[3.485863960601927, -0.7883076520663903] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E25	${\displaystyle{\displaystyle\mathrm{Bi}\left(z\right)=\frac{1}{3^{1/6}\Gamma\left(\tfrac{2}{3}\right)}e^{-\zeta}{{}_{1}F_{1}}\left(\tfrac{1}{6};\tfrac{1}{3};2\zeta\right)+\frac{3^{5/6}}{2^{2/3}\Gamma\left(\tfrac{1}{3}\right)}\zeta^{2/3}e^{-\zeta}{{}_{1}F_{1}}\left(\tfrac{5}{6};\tfrac{5}{3};2\zeta\right)}}$	AiryBi(z)=(1)/((3)^(1/ 6)* GAMMA((2)/(3)))*exp(-(2)/(3)*(z)^((3)/(2)))*hypergeom([(1)/(6)], [(1)/(3)], 2*(2)/(3)*(z)^((3)/(2)))+((3)^(5/ 6))/((2)^(2/ 3)* GAMMA((1)/(3)))*(2)/(3)*((z)^((3)/(2)))^(2/ 3)* exp(-(2)/(3)*(z)^((3)/(2)))*hypergeom([(5)/(6)], [(5)/(3)], 2*(2)/(3)*(z)^((3)/(2)))	AiryBi[z]=Divide[1,(3)^(1/ 6)* Gamma[Divide[2,3]]]*Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricPFQ[{Divide[1,6]}, {Divide[1,3]}, 2*Divide[2,3]*(z)^(Divide[3,2])]+Divide[(3)^(5/ 6),(2)^(2/ 3)* Gamma[Divide[1,3]]]*Divide[2,3]*((z)^(Divide[3,2]))^(2/ 3)* Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricPFQ[{Divide[5,6]}, {Divide[5,3]}, 2*Divide[2,3]*(z)^(Divide[3,2])]	Failure	Failure	Fail .147168161e-1+.712025224e-1*I <- {z = 2^(1/2)+I*2^(1/2)} .147168161e-1-.712025224e-1*I <- {z = 2^(1/2)-I*2^(1/2)} -1.474010305-1.772597131*I <- {z = -2^(1/2)-I*2^(1/2)} -1.474010305+1.772597131*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[0.014716817548916183, 0.07120252241962582] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[0.014716817548916183, -0.07120252241962582] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-1.474010305021376, -1.7725971311665962] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-1.474010305021376, 1.7725971311665962] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.6.E26	${\displaystyle{\displaystyle\mathrm{Bi}'\left(z\right)=\frac{3^{1/6}}{\Gamma\left(\tfrac{1}{3}\right)}e^{-\zeta}{{}_{1}F_{1}}\left(-\tfrac{1}{6};-\tfrac{1}{3};2\zeta\right)+\frac{3^{7/6}}{2^{7/3}\Gamma\left(\tfrac{2}{3}\right)}\zeta^{4/3}e^{-\zeta}{{}_{1}F_{1}}\left(\tfrac{7}{6};\tfrac{7}{3};2\zeta\right)}}$	subs( temp=z, diff( AiryBi(temp), temp$(1) ) )=((3)^(1/ 6))/(GAMMA((1)/(3)))*exp(-(2)/(3)*(z)^((3)/(2)))*hypergeom([-(1)/(6)], [-(1)/(3)], 2*(2)/(3)*(z)^((3)/(2)))+((3)^(7/ 6))/((2)^(7/ 3)* GAMMA((2)/(3)))*(2)/(3)*((z)^((3)/(2)))^(4/ 3)* exp(-(2)/(3)*(z)^((3)/(2)))*hypergeom([(7)/(6)], [(7)/(3)], 2*(2)/(3)*(z)^((3)/(2)))	(D[AiryBi[temp], {temp, 1}]/.temp-> z)=Divide[(3)^(1/ 6),Gamma[Divide[1,3]]]*Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricPFQ[{-Divide[1,6]}, {-Divide[1,3]}, 2*Divide[2,3]*(z)^(Divide[3,2])]+Divide[(3)^(7/ 6),(2)^(7/ 3)* Gamma[Divide[2,3]]]*Divide[2,3]*((z)^(Divide[3,2]))^(4/ 3)* Exp[-Divide[2,3]*(z)^(Divide[3,2])]*HypergeometricPFQ[{Divide[7,6]}, {Divide[7,3]}, 2*Divide[2,3]*(z)^(Divide[3,2])]	Failure	Failure	Fail .522018891e-1-.1117022869*I <- {z = 2^(1/2)+I*2^(1/2)} .522018891e-1+.1117022869*I <- {z = 2^(1/2)-I*2^(1/2)} 2.583360720+2.078187022*I <- {z = -2^(1/2)-I*2^(1/2)} 2.583360720-2.078187022*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[0.0522018904439151, -0.11170228512421254] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[0.0522018904439151, 0.11170228512421254] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[2.5833607207543476, 2.078187024166196] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[2.5833607207543476, -2.078187024166196] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.7#Ex3	${\displaystyle{\displaystyle\mathrm{Ai}\left(x\right)<=\frac{e^{-\xi}}{2\sqrt{\pi}x^{1/4}}}}$	AiryAi(x)< =(exp(- xi))/(2*sqrt(Pi)*(x)^(1/ 4))	AiryAi[x]< =Divide[Exp[- \[Xi]],2*Sqrt[Pi]*(x)^(1/ 4)]	Failure	Failure	Successful	Successful
9.7#Ex4	${\displaystyle{\displaystyle|\mathrm{Ai}'\left(x\right)|<=\frac{x^{1/4}e^{-\xi}}{2\sqrt{\pi}}\left(1+\frac{7}{72\xi}\right)}}$	abs(subs( temp=x, diff( AiryAi(temp), temp$(1) ) ))< =((x)^(1/ 4)* exp(- xi))/(2*sqrt(Pi))*(1 +(7)/(72*xi))	Abs[D[AiryAi[temp], {temp, 1}]/.temp-> x]< =Divide[(x)^(1/ 4)* Exp[- \[Xi]],2*Sqrt[Pi]]*(1 +Divide[7,72*\[Xi]])	Failure	Failure	Successful	Successful
9.7#Ex5	${\displaystyle{\displaystyle\mathrm{Bi}\left(x\right)<=\frac{{\mathrm{e}^{\xi}}}{\sqrt{\pi}x^{1/4}}\left(1+\left(\chi(\tfrac{7}{6})+1\right)\frac{5}{72\xi}\right)}}$	AiryBi(x)< =(exp(xi))/(sqrt(Pi)*(x)^(1/ 4))*(1 +(chi*((7)/(6))+ 1)*(5)/(72*xi))	AiryBi[x]< =Divide[Exp[\[Xi]],Sqrt[Pi]*(x)^(1/ 4)]*(1 +(\[Chi]*(Divide[7,6])+ 1)*Divide[5,72*\[Xi]])	Failure	Failure	Successful	Successful
9.7#Ex6	${\displaystyle{\displaystyle\mathrm{Bi}'\left(x\right)<=\frac{x^{1/4}e^{\xi}}{\sqrt{\pi}}\left(1+\left(\frac{\pi}{2}+1\right)\frac{7}{72\xi}\right)}}$	subs( temp=x, diff( AiryBi(temp), temp$(1) ) )< =((x)^(1/ 4)* exp(xi))/(sqrt(Pi))*(1 +((Pi)/(2)+ 1)*(7)/(72*xi))	(D[AiryBi[temp], {temp, 1}]/.temp-> x)< =Divide[(x)^(1/ 4)* Exp[\[Xi]],Sqrt[Pi]]*(1 +(Divide[Pi,2]+ 1)*Divide[7,72*\[Xi]])	Failure	Failure	Successful	Successful
9.7.E17	${\displaystyle{\displaystyle\begin{cases}1,&|\operatorname{ph}z|<=\tfrac{1}{3}\pi,\\ \min\left(|\csc\left(\operatorname{ph}\zeta\right)|,\chi(n+\sigma)+1\right),&\tfrac{1}{3}\pi}}\)\@add@PDF@RDFa@triples\end{document}\end{cases}$			Error	Error	-	-
9.7.E18	${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{e^{-\zeta}}{2\sqrt{\pi}z^{1/4}}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{u_{k}}{\zeta^{k}}+R_{n}(z)\right)}}$	AiryAi(z)=(exp(-(2)/(3)*(z)^((3)/(2))))/(2*sqrt(Pi)*(z)^(1/ 4))*(sum((- 1)^(k)*(u[k])/((2)/(3)*((z)^((3)/(2)))^(k)), k = 0..n - 1)+ R[n]*(z))	AiryAi[z]=Divide[Exp[-Divide[2,3]*(z)^(Divide[3,2])],2*Sqrt[Pi]*(z)^(1/ 4)]*(Sum[(- 1)^(k)*Divide[Subscript[u, k],Divide[2,3]*((z)^(Divide[3,2]))^(k)], {k, 0, n - 1}]+ Subscript[R, n]*(z))	Failure	Failure	Skip	Skip
9.7.E19	${\displaystyle{\displaystyle\mathrm{Ai}'\left(z\right)=-\frac{z^{1/4}e^{-\zeta}}{2\sqrt{\pi}}\left(\sum_{k=0}^{n-1}(-1)^{k}\frac{v_{k}}{\zeta^{k}}+S_{n}(z)\right)}}$	subs( temp=z, diff( AiryAi(temp), temp$(1) ) )= -((z)^(1/ 4)* exp(-(2)/(3)*(z)^((3)/(2))))/(2*sqrt(Pi))*(sum((- 1)^(k)*(v[k])/((2)/(3)*((z)^((3)/(2)))^(k)), k = 0..n - 1)+ S[n]*(z))	(D[AiryAi[temp], {temp, 1}]/.temp-> z)= -Divide[(z)^(1/ 4)* Exp[-Divide[2,3]*(z)^(Divide[3,2])],2*Sqrt[Pi]]*(Sum[(- 1)^(k)*Divide[Subscript[v, k],Divide[2,3]*((z)^(Divide[3,2]))^(k)], {k, 0, n - 1}]+ Subscript[S, n]*(z))	Failure	Failure	Skip	Skip
9.7.E22	${\displaystyle{\displaystyle G_{p}\left(z\right)=\frac{e^{z}}{2\pi}\Gamma\left(p\right)\Gamma\left(1-p,z\right)}}$	(exp(z)/(2*Pi))*GAMMA(p)*GAMMA(1-p,z)=(exp(z))/(2*Pi)*GAMMA(p)*GAMMA(1 - p, z)	Error	Successful	Error	-	-
9.8.E1	${\displaystyle{\displaystyle\mathrm{Ai}\left(x\right)=M\left(x\right)\sin\theta\left(x\right)}}$	AiryAi(x)= sqrt(AiryAi(x)^2+AiryBi(x)^2)*sin(arctan(AiryAi(x)/AiryBi(x)))	AiryAi[x]= Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*Sin[ArcTan[Divide[AiryAi[x], AiryBi[x]]]]	Failure	Failure	Successful	Successful
9.8.E2	${\displaystyle{\displaystyle\mathrm{Bi}\left(x\right)=M\left(x\right)\cos\theta\left(x\right)}}$	AiryBi(x)= sqrt(AiryAi(x)^2+AiryBi(x)^2)*cos(arctan(AiryAi(x)/AiryBi(x)))	AiryBi[x]= Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*Cos[ArcTan[Divide[AiryAi[x], AiryBi[x]]]]	Failure	Failure	Successful	Successful
9.8.E3	${\displaystyle{\displaystyle M\left(x\right)=\sqrt{{\mathrm{Ai}^{2}}\left(x\right)+{\mathrm{Bi}^{2}}\left(x\right)}}}$	sqrt(AiryAi(x)^2+AiryBi(x)^2)=sqrt((AiryAi(x))^(2)+ (AiryBi(x))^(2))	Sqrt[AiryAi[x]^2 + AiryBi[x]^2]=Sqrt[(AiryAi[x])^(2)+ (AiryBi[x])^(2)]	Successful	Successful	-	-
9.8.E4	${\displaystyle{\displaystyle\theta\left(x\right)=\operatorname{arctan}\left(\mathrm{Ai}\left(x\right)/\mathrm{Bi}\left(x\right)\right)}}$	arctan(AiryAi(x)/AiryBi(x))= arctan(AiryAi(x)/ AiryBi(x))	ArcTan[Divide[AiryAi[x], AiryBi[x]]]= ArcTan[AiryAi[x]/ AiryBi[x]]	Successful	Successful	-	-
9.8.E5	${\displaystyle{\displaystyle\mathrm{Ai}'\left(x\right)=N\left(x\right)\sin\phi\left(x\right)}}$	subs( temp=x, diff( AiryAi(temp), temp$(1) ) )= sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)*sin(arctan(AiryAi(1, x)/AiryBi(1, x)))	(D[AiryAi[temp], {temp, 1}]/.temp-> x)= Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]*Sin[ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]]	Failure	Failure	Successful	Successful
9.8.E6	${\displaystyle{\displaystyle\mathrm{Bi}'\left(x\right)=N\left(x\right)\cos\phi\left(x\right)}}$	subs( temp=x, diff( AiryBi(temp), temp$(1) ) )= sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)*cos(arctan(AiryAi(1, x)/AiryBi(1, x)))	(D[AiryBi[temp], {temp, 1}]/.temp-> x)= Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]*Cos[ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]]	Failure	Failure	Successful	Successful
9.8.E7	${\displaystyle{\displaystyle N\left(x\right)=\sqrt{{\mathrm{Ai}'^{2}}\left(x\right)+{\mathrm{Bi}'^{2}}\left(x\right)}}}$	sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)=sqrt((subs( temp=x, diff( AiryAi(temp), temp$(1) ) ))^(2)+ (subs( temp=x, diff( AiryBi(temp), temp$(1) ) ))^(2))	Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]=Sqrt[((D[AiryAi[temp], {temp, 1}]/.temp-> x))^(2)+ ((D[AiryBi[temp], {temp, 1}]/.temp-> x))^(2)]	Successful	Successful	-	-
9.8.E8	${\displaystyle{\displaystyle\phi\left(x\right)=\operatorname{arctan}\left(\mathrm{Ai}'\left(x\right)/\mathrm{Bi}'\left(x\right)\right)}}$	arctan(AiryAi(1, x)/AiryBi(1, x))= arctan(subs( temp=x, diff( AiryAi(temp), temp$(1) ) )/ subs( temp=x, diff( AiryBi(temp), temp$(1) ) ))	ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]= ArcTan[(D[AiryAi[temp], {temp, 1}]/.temp-> x)/ (D[AiryBi[temp], {temp, 1}]/.temp-> x)]	Successful	Successful	-	-
9.8.E9	${\displaystyle{\displaystyle|x|^{1/2}{M^{2}}\left(x\right)=\tfrac{1}{2}\xi\left({J_{1/3}^{2}}\left(\xi\right)+{Y_{1/3}^{2}}\left(\xi\right)\right)}}$	(abs(x))^(1/ 2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)=(1)/(2)*xi*((BesselJ(1/ 3, xi))^(2)+ (BesselY(1/ 3, xi))^(2))	(Abs[x])^(1/ 2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)=Divide[1,2]*\[Xi]*((BesselJ[1/ 3, \[Xi]])^(2)+ (BesselY[1/ 3, \[Xi]])^(2))	Failure	Failure	Fail 1.159089025-.4715106810e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1} 15.06764807-.4715106810e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2} 340.9777186-.4715106810e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3} 1.159089025+.4715106810e-2*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1} ... skip entries to safe data	Fail Complex[1.1590890245070966, -0.004715107328741586] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[15.06764807713232, -0.004715107328741586] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[340.9777188366776, -0.004715107328741586] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[1.1590890245070966, 0.004715107328741586] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data
9.8.E10	${\displaystyle{\displaystyle|x|^{-1/2}{N^{2}}\left(x\right)=\tfrac{1}{2}\xi\left({J_{2/3}^{2}}\left(\xi\right)+{Y_{2/3}^{2}}\left(\xi\right)\right)}}$	(abs(x))^(- 1/ 2)* (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)=(1)/(2)*xi*((BesselJ(2/ 3, xi))^(2)+ (BesselY(2/ 3, xi))^(2))	(Abs[x])^(- 1/ 2)* (Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)=Divide[1,2]*\[Xi]*((BesselJ[2/ 3, \[Xi]])^(2)+ (BesselY[2/ 3, \[Xi]])^(2))	Failure	Failure	Fail .5749530917+.6794393049e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1} 11.57260149+.6794393049e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2} 303.0362324+.6794393049e-2*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3} .5749530917-.6794393049e-2*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1} ... skip entries to safe data	Fail Complex[0.5749530907924223, 0.0067943920267909685] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[11.572601490351364, 0.0067943920267909685] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[303.0362323510325, 0.0067943920267909685] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[0.5749530907924223, -0.0067943920267909685] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data
9.8.E11	${\displaystyle{\displaystyle\theta\left(x\right)=\tfrac{2}{3}\pi+\operatorname{arctan}\left(Y_{1/3}\left(\xi\right)/J_{1/3}\left(\xi\right)\right)}}$	arctan(AiryAi(x)/AiryBi(x))=(2)/(3)*Pi + arctan(BesselY(1/ 3, xi)/ BesselJ(1/ 3, xi))	ArcTan[Divide[AiryAi[x], AiryBi[x]]]=Divide[2,3]*Pi + ArcTan[BesselY[1/ 3, \[Xi]]/ BesselJ[1/ 3, \[Xi]]]	Failure	Failure	Fail -2.062235934-1.435552558*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1} -2.163232204-1.435552558*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2} -2.173351447-1.435552558*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3} -2.062235934+1.435552558*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1} ... skip entries to safe data	Fail Complex[-2.062235934109286, -1.435552557338311] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-2.163232204380712, -1.435552557338311] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-2.17335144762396, -1.435552557338311] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-2.062235934109286, 1.435552557338311] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data
9.8.E12	${\displaystyle{\displaystyle\phi\left(x\right)=\tfrac{1}{3}\pi+\operatorname{arctan}\left(Y_{2/3}\left(\xi\right)/J_{2/3}\left(\xi\right)\right)}}$	arctan(AiryAi(1, x)/AiryBi(1, x))=(1)/(3)*Pi + arctan(BesselY(2/ 3, xi)/ BesselJ(2/ 3, xi))	ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]=Divide[1,3]*Pi + ArcTan[BesselY[2/ 3, \[Xi]]/ BesselJ[2/ 3, \[Xi]]]	Failure	Failure	Fail -.8340487847-1.384157839*I <- {xi = 2^(1/2)+I*2^(1/2), x = 1} -.6779445534-1.384157839*I <- {xi = 2^(1/2)+I*2^(1/2), x = 2} -.6655182693-1.384157839*I <- {xi = 2^(1/2)+I*2^(1/2), x = 3} -.8340487847+1.384157839*I <- {xi = 2^(1/2)-I*2^(1/2), x = 1} ... skip entries to safe data	Fail Complex[-0.8340487867218234, -1.3841578383770126] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-0.6779445554392751, -1.3841578383770126] <- {Rule[x, 2], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-0.6655182713247128, -1.3841578383770126] <- {Rule[x, 3], Rule[ξ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-0.8340487867218234, 1.3841578383770126] <- {Rule[x, 1], Rule[ξ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data
9.8.E13	${\displaystyle{\displaystyle M\left(x\right)N\left(x\right)\sin\left(\theta\left(x\right)-\phi\left(x\right)\right)=\pi^{-1}}}$	sqrt(AiryAi(x)^2+AiryBi(x)^2)*sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)*sin(arctan(AiryAi(x)/AiryBi(x))- arctan(AiryAi(1, x)/AiryBi(1, x)))= (Pi)^(- 1)	Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]*Sin[ArcTan[Divide[AiryAi[x], AiryBi[x]]]- ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]]= (Pi)^(- 1)	Failure	Failure	Successful	Successful
9.8#Ex1	${\displaystyle{\displaystyle{M^{2}}\left(x\right)\theta'\left(x\right)=-\pi^{-1}}}$	(sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)* subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) )= - (Pi)^(- 1)	(Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)* (D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x)= - (Pi)^(- 1)	Failure	Successful	Successful	-
9.8#Ex2	${\displaystyle{\displaystyle{N^{2}}\left(x\right)\phi'\left(x\right)=\pi^{-1}x}}$	(sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)* subs( temp=x, diff( arctan(AiryAi(1, temp)/AiryBi(1, temp)), temp$(1) ) )= (Pi)^(- 1)* x	(Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)* (D[ArcTan[Divide[AiryAiPrime[temp], AiryBiPrime[temp]]], {temp, 1}]/.temp-> x)= (Pi)^(- 1)* x	Failure	Successful	Successful	-
9.8#Ex3	${\displaystyle{\displaystyle N\left(x\right)N'\left(x\right)=xM\left(x\right)M'\left(x\right)}}$	sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2)*subs( temp=x, diff( sqrt(AiryAi(1, temp)^2+AiryBi(1, temp)^2), temp$(1) ) )= x*sqrt(AiryAi(x)^2+AiryBi(x)^2)*subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) )	Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2]*(D[Sqrt[AiryAiPrime[temp]^2 + AiryBiPrime[temp]^2], {temp, 1}]/.temp-> x)= x*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*(D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x)	Successful	Successful	-	-
9.8.E15	${\displaystyle{\displaystyle{N^{2}}\left(x\right)={M'^{2}}\left(x\right)+{M^{2}}\left(x\right){\theta'^{2}}\left(x\right)}}$	(sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)= (subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ))^(2)+ (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)* (subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) ))^(2)	(Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)= ((D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x))^(2)+ (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)* ((D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x))^(2)	Successful	Successful	-	-
9.8.E15	${\displaystyle{\displaystyle{M'^{2}}\left(x\right)+{M^{2}}\left(x\right){\theta'^{2}}\left(x\right)={M'^{2}}(x)+\pi^{-2}{M^{-2}}\left(x\right)}}$	(subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ))^(2)+ (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)* (subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) ))^(2)= (subs( temp=(x), diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ))^(2)+ (Pi)^(- 2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(- 2)	((D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x))^(2)+ (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)* ((D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x))^(2)= ((D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> (x)))^(2)+ (Pi)^(- 2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(- 2)	Failure	Successful	Successful	-
9.8.E16	${\displaystyle{\displaystyle x^{2}{M^{2}}\left(x\right)={N'^{2}}\left(x\right)+{N^{2}}\left(x\right){\phi'^{2}}\left(x\right)}}$	(x)^(2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)= (subs( temp=x, diff( sqrt(AiryAi(1, temp)^2+AiryBi(1, temp)^2), temp$(1) ) ))^(2)+ (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)* (subs( temp=x, diff( arctan(AiryAi(1, temp)/AiryBi(1, temp)), temp$(1) ) ))^(2)	(x)^(2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)= ((D[Sqrt[AiryAiPrime[temp]^2 + AiryBiPrime[temp]^2], {temp, 1}]/.temp-> x))^(2)+ (Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)* ((D[ArcTan[Divide[AiryAiPrime[temp], AiryBiPrime[temp]]], {temp, 1}]/.temp-> x))^(2)	Successful	Successful	-	-
9.8.E16	${\displaystyle{\displaystyle{N'^{2}}\left(x\right)+{N^{2}}\left(x\right){\phi'^{2}}\left(x\right)={N'^{2}}\left(x\right)+\pi^{-2}x^{2}{N^{-2}}\left(x\right)}}$	(subs( temp=x, diff( sqrt(AiryAi(1, temp)^2+AiryBi(1, temp)^2), temp$(1) ) ))^(2)+ (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(2)* (subs( temp=x, diff( arctan(AiryAi(1, temp)/AiryBi(1, temp)), temp$(1) ) ))^(2)= (subs( temp=x, diff( sqrt(AiryAi(1, temp)^2+AiryBi(1, temp)^2), temp$(1) ) ))^(2)+ (Pi)^(- 2)* (x)^(2)* (sqrt(AiryAi(1, x)^2+AiryBi(1, x)^2))^(- 2)	((D[Sqrt[AiryAiPrime[temp]^2 + AiryBiPrime[temp]^2], {temp, 1}]/.temp-> x))^(2)+ (Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(2)* ((D[ArcTan[Divide[AiryAiPrime[temp], AiryBiPrime[temp]]], {temp, 1}]/.temp-> x))^(2)= ((D[Sqrt[AiryAiPrime[temp]^2 + AiryBiPrime[temp]^2], {temp, 1}]/.temp-> x))^(2)+ (Pi)^(- 2)* (x)^(2)* (Sqrt[AiryAiPrime[x]^2 + AiryBiPrime[x]^2])^(- 2)	Failure	Successful	Successful	-
9.8.E17	${\displaystyle{\displaystyle\tan\left(\theta\left(x\right)-\phi\left(x\right)\right)=1/(\pi M\left(x\right)M'\left(x\right))}}$	tan(arctan(AiryAi(x)/AiryBi(x))- arctan(AiryAi(1, x)/AiryBi(1, x)))= 1/(Pi*sqrt(AiryAi(x)^2+AiryBi(x)^2)*subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ))	Tan[ArcTan[Divide[AiryAi[x], AiryBi[x]]]- ArcTan[Divide[AiryAiPrime[x], AiryBiPrime[x]]]]= 1/(Pi*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*(D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x))	Failure	Successful	Successful	-
9.8.E17	${\displaystyle{\displaystyle 1/(\pi M\left(x\right)M'\left(x\right))=-M\left(x\right)\theta'\left(x\right)/M'\left(x\right)}}$	1/(Pi*sqrt(AiryAi(x)^2+AiryBi(x)^2)*subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ))= - sqrt(AiryAi(x)^2+AiryBi(x)^2)*subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) )/ subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) )	1/(Pi*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*(D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x))= - Sqrt[AiryAi[x]^2 + AiryBi[x]^2]*(D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x)/ (D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x)	Failure	Successful	Successful	-
9.8#Ex4	${\displaystyle{\displaystyle M''\left(x\right)=xM\left(x\right)+\pi^{-2}{M^{-3}}\left(x\right)}}$	subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(2) ) )= x*sqrt(AiryAi(x)^2+AiryBi(x)^2)+ (Pi)^(- 2)* (sqrt(AiryAi(x)^2+AiryBi(x)^2))^(- 3)	(D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 2}]/.temp-> x)= x*Sqrt[AiryAi[x]^2 + AiryBi[x]^2]+ (Pi)^(- 2)* (Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(- 3)	Failure	Successful	Successful	-
9.8#Ex5	${\displaystyle{\displaystyle{M^{2}}'''\left(x\right)-4x{M^{2}}'\left(x\right)-2{M^{2}}\left(x\right)=0}}$	(subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(3) ) ))^(2)- 4*x*(subs( temp=x, diff( sqrt(AiryAi(temp)^2+AiryBi(temp)^2), temp$(1) ) ))^(2)- 2*(sqrt(AiryAi(x)^2+AiryBi(x)^2))^(2)= 0	((D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 3}]/.temp-> x))^(2)- 4*x*((D[Sqrt[AiryAi[temp]^2 + AiryBi[temp]^2], {temp, 1}]/.temp-> x))^(2)- 2*(Sqrt[AiryAi[x]^2 + AiryBi[x]^2])^(2)= 0	Failure	Failure	Fail -2.268412261 <- {x = 1} -24.26674995 <- {x = 2} 157.2405245 <- {x = 3}	Fail -2.2684122541643257 <- {Rule[x, 1]} -24.266750191340662 <- {Rule[x, 2]} 157.2404952502784 <- {Rule[x, 3]}
9.8.E19	${\displaystyle{\displaystyle{\theta'^{2}}\left(x\right)+\tfrac{1}{2}(\theta'''\left(x\right)/\theta'\left(x\right))-\tfrac{3}{4}(\theta''\left(x\right)/\theta'\left(x\right))^{2}=-x}}$	(subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) ))^(2)+(1)/(2)*(subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(3) ) )/ subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) ))-(3)/(4)*(subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(2) ) )/ subs( temp=x, diff( arctan(AiryAi(temp)/AiryBi(temp)), temp$(1) ) ))^(2)= - x	((D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x))^(2)+Divide[1,2]*((D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 3}]/.temp-> x)/ (D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x))-Divide[3,4]*(((D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 2}]/.temp-> x)/ (D[ArcTan[Divide[AiryAi[temp], AiryBi[temp]]], {temp, 1}]/.temp-> x)))^(2)= - x	Successful	Successful	-	-
9.10.E1	${\displaystyle{\displaystyle\int_{z}^{\infty}\mathrm{Ai}\left(t\right)\mathrm{d}t=\pi\left(\mathrm{Ai}\left(z\right)\mathrm{Gi}'\left(z\right)-\mathrm{Ai}'\left(z\right)\mathrm{Gi}\left(z\right)\right)}}$	int(AiryAi(t), t = z..infinity)= Pi*(AiryAi(z)*subs( temp=z, diff( AiryBi(temp)*(int(AiryAi(t), t = (temp) .. infinity))+AiryAi(temp)*(int(AiryBi(t), t = 0 .. (temp))), temp$(1) ) )- subs( temp=z, diff( AiryAi(temp), temp$(1) ) )*AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z))))	Integrate[AiryAi[t], {t, z, Infinity}]= Pi*(AiryAi[z]*(D[ScorerGi[temp], {temp, 1}]/.temp-> z)- (D[AiryAi[temp], {temp, 1}]/.temp-> z)*ScorerGi[z])	Failure	Failure	Skip	Successful
9.10.E2	${\displaystyle{\displaystyle\int_{-\infty}^{z}\mathrm{Ai}\left(t\right)\mathrm{d}t=\pi\left(\mathrm{Ai}\left(z\right)\mathrm{Hi}'\left(z\right)-\mathrm{Ai}'\left(z\right)\mathrm{Hi}\left(z\right)\right)}}$	int(AiryAi(t), t = - infinity..z)= Pi*(AiryAi(z)*subs( temp=z, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) )- subs( temp=z, diff( AiryAi(temp), temp$(1) ) )*AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))))	Integrate[AiryAi[t], {t, - Infinity, z}]= Pi*(AiryAi[z]*(D[ScorerHi[temp], {temp, 1}]/.temp-> z)- (D[AiryAi[temp], {temp, 1}]/.temp-> z)*ScorerHi[z])	Failure	Failure	Skip	Successful
9.10.E3	${\displaystyle{\displaystyle\int_{-\infty}^{z}\mathrm{Bi}\left(t\right)\mathrm{d}t=\int_{0}^{z}\mathrm{Bi}\left(t\right)\mathrm{d}t}}$	int(AiryBi(t), t = - infinity..z)= int(AiryBi(t), t = 0..z)	Integrate[AiryBi[t], {t, - Infinity, z}]= Integrate[AiryBi[t], {t, 0, z}]	Successful	Failure	-	Successful
9.10.E3	${\displaystyle{\displaystyle\pi\left(\mathrm{Bi}'\left(z\right)\mathrm{Gi}\left(z\right)-\mathrm{Bi}\left(z\right)\mathrm{Gi}'\left(z\right)\right)\\ =\pi\left(\mathrm{Bi}\left(z\right)\mathrm{Hi}'\left(z\right)-\mathrm{Bi}'\left(z\right)\mathrm{Hi}\left(z\right)\right)}}$	Pi*(subs( temp=z, diff( AiryBi(temp), temp$(1) ) )*AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))- AiryBi(z)*subs( temp=z, diff( AiryBi(temp)*(int(AiryAi(t), t = (temp) .. infinity))+AiryAi(temp)*(int(AiryBi(t), t = 0 .. (temp))), temp$(1) ) ))= Pi*(AiryBi(z)*subs( temp=z, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) )- subs( temp=z, diff( AiryBi(temp), temp$(1) ) )*AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z))))	Pi*((D[AiryBi[temp], {temp, 1}]/.temp-> z)*ScorerGi[z]- AiryBi[z]*(D[ScorerGi[temp], {temp, 1}]/.temp-> z))= Pi*(AiryBi[z]*(D[ScorerHi[temp], {temp, 1}]/.temp-> z)- (D[AiryBi[temp], {temp, 1}]/.temp-> z)*ScorerHi[z])	Error	Error	-	-
9.10#Ex1	${\displaystyle{\displaystyle\int_{0}^{\infty}\mathrm{Ai}\left(t\right)\mathrm{d}t=\tfrac{1}{3}}}$	int(AiryAi(t), t = 0..infinity)=(1)/(3)	Integrate[AiryAi[t], {t, 0, Infinity}]=Divide[1,3]	Successful	Successful	-	-
9.10#Ex2	${\displaystyle{\displaystyle\int_{-\infty}^{0}\mathrm{Ai}\left(t\right)\mathrm{d}t=\tfrac{2}{3}}}$	int(AiryAi(t), t = - infinity..0)=(2)/(3)	Integrate[AiryAi[t], {t, - Infinity, 0}]=Divide[2,3]	Successful	Failure	-	Successful
9.10.E12	${\displaystyle{\displaystyle\int_{-\infty}^{0}\mathrm{Bi}\left(t\right)\mathrm{d}t=0}}$	int(AiryBi(t), t = - infinity..0)= 0	Integrate[AiryBi[t], {t, - Infinity, 0}]= 0	Successful	Failure	-	Successful
9.10.E13	${\displaystyle{\displaystyle\int_{-\infty}^{\infty}e^{pt}\mathrm{Ai}\left(t\right)\mathrm{d}t=e^{p^{3}/3}}}$	int(exp(p*t)*AiryAi(t), t = - infinity..infinity)= exp((p)^(3)/ 3)	Integrate[Exp[p*t]*AiryAi[t], {t, - Infinity, Infinity}]= Exp[(p)^(3)/ 3]	Failure	Failure	Skip	Error
9.10.E14	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-pt}\mathrm{Ai}\left(t\right)\mathrm{d}t=e^{-p^{3}/3}\left(\frac{1}{3}-\frac{p{{}_{1}F_{1}}\left(\tfrac{1}{3};\tfrac{4}{3};\tfrac{1}{3}p^{3}\right)}{3^{4/3}\Gamma\left(\tfrac{4}{3}\right)}+\frac{p^{2}{{}_{1}F_{1}}\left(\tfrac{2}{3};\tfrac{5}{3};\tfrac{1}{3}p^{3}\right)}{3^{5/3}\Gamma\left(\tfrac{5}{3}\right)}\right)}}$	int(exp(- p*t)*AiryAi(t), t = 0..infinity)= exp(- (p)^(3)/ 3)*((1)/(3)-(p*hypergeom([(1)/(3)], [(4)/(3)], (1)/(3)*(p)^(3)))/((3)^(4/ 3)* GAMMA((4)/(3)))+((p)^(2)* hypergeom([(2)/(3)], [(5)/(3)], (1)/(3)*(p)^(3)))/((3)^(5/ 3)* GAMMA((5)/(3))))	Integrate[Exp[- p*t]*AiryAi[t], {t, 0, Infinity}]= Exp[- (p)^(3)/ 3]*(Divide[1,3]-Divide[p*HypergeometricPFQ[{Divide[1,3]}, {Divide[4,3]}, Divide[1,3]*(p)^(3)],(3)^(4/ 3)* Gamma[Divide[4,3]]]+Divide[(p)^(2)* HypergeometricPFQ[{Divide[2,3]}, {Divide[5,3]}, Divide[1,3]*(p)^(3)],(3)^(5/ 3)* Gamma[Divide[5,3]]])	Successful	Failure	-	Successful
9.10.E15	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-pt}\mathrm{Ai}\left(-t\right)\mathrm{d}t={\frac{1}{3}e^{p^{3}/3}\left(\frac{\Gamma\left(\tfrac{1}{3},\tfrac{1}{3}p^{3}\right)}{\Gamma\left(\tfrac{1}{3}\right)}+\frac{\Gamma\left(\tfrac{2}{3},\tfrac{1}{3}p^{3}\right)}{\Gamma\left(\tfrac{2}{3}\right)}\right)}}}$	int(exp(- p*t)*AiryAi(- t), t = 0..infinity)=(1)/(3)*exp((p)^(3)/ 3)*((GAMMA((1)/(3), (1)/(3)*(p)^(3)))/(GAMMA((1)/(3)))+(GAMMA((2)/(3), (1)/(3)*(p)^(3)))/(GAMMA((2)/(3))))	Integrate[Exp[- p*t]*AiryAi[- t], {t, 0, Infinity}]=Divide[1,3]*Exp[(p)^(3)/ 3]*(Divide[Gamma[Divide[1,3], Divide[1,3]*(p)^(3)],Gamma[Divide[1,3]]]+Divide[Gamma[Divide[2,3], Divide[1,3]*(p)^(3)],Gamma[Divide[2,3]]])	Failure	Failure	Skip	Error
9.10.E16	${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-pt}\mathrm{Bi}\left(-t\right)\mathrm{d}t={\frac{1}{\sqrt{3}}e^{p^{3}/3}\left(\frac{\Gamma\left(\tfrac{2}{3},\tfrac{1}{3}p^{3}\right)}{\Gamma\left(\tfrac{2}{3}\right)}-\frac{\Gamma\left(\tfrac{1}{3},\tfrac{1}{3}p^{3}\right)}{\Gamma\left(\tfrac{1}{3}\right)}\right)}}}$	int(exp(- p*t)*AiryBi(- t), t = 0..infinity)=(1)/(sqrt(3))*exp((p)^(3)/ 3)*((GAMMA((2)/(3), (1)/(3)*(p)^(3)))/(GAMMA((2)/(3)))-(GAMMA((1)/(3), (1)/(3)*(p)^(3)))/(GAMMA((1)/(3))))	Integrate[Exp[- p*t]*AiryBi[- t], {t, 0, Infinity}]=Divide[1,Sqrt[3]]*Exp[(p)^(3)/ 3]*(Divide[Gamma[Divide[2,3], Divide[1,3]*(p)^(3)],Gamma[Divide[2,3]]]-Divide[Gamma[Divide[1,3], Divide[1,3]*(p)^(3)],Gamma[Divide[1,3]]])	Failure	Failure	Skip	Error
9.10.E18	${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{3z^{5/4}e^{-(2/3)z^{3/2}}}{4\pi}\*\int_{0}^{\infty}\frac{t^{-3/4}e^{-(2/3)t^{3/2}}\mathrm{Ai}\left(t\right)}{z^{3/2}+t^{3/2}}\mathrm{d}t}}$	AiryAi(z)=(3*(z)^(5/ 4)* exp(-(2/ 3)* (z)^(3/ 2)))/(4*Pi)* int(((t)^(- 3/ 4)* exp(-(2/ 3)* (t)^(3/ 2))*AiryAi(t))/((z)^(3/ 2)+ (t)^(3/ 2)), t = 0..infinity)	AiryAi[z]=Divide[3*(z)^(5/ 4)* Exp[-(2/ 3)* (z)^(3/ 2)],4*Pi]* Integrate[Divide[(t)^(- 3/ 4)* Exp[-(2/ 3)* (t)^(3/ 2)]*AiryAi[t],(z)^(3/ 2)+ (t)^(3/ 2)], {t, 0, Infinity}]	Error	Failure	-	Error
9.10#Ex3	${\displaystyle{\displaystyle\mathrm{Ai}\left(z\right)=\frac{z^{5/4}e^{-(2/3)z^{3/2}}}{2^{7/2}\pi}\*\int_{0}^{\infty}\frac{t^{-1/2}e^{-(2/3)t^{3/2}}\mathrm{Ai}\left(t\right)}{z^{3/2}+t^{3/2}}\mathrm{d}t}}$	AiryAi(z)=((z)^(5/ 4)* exp(-(2/ 3)* (z)^(3/ 2)))/((2)^(7/ 2)* Pi)* int(((t)^(- 1/ 2)* exp(-(2/ 3)* (t)^(3/ 2))*AiryAi(t))/((z)^(3/ 2)+ (t)^(3/ 2)), t = 0..infinity)	AiryAi[z]=Divide[(z)^(5/ 4)* Exp[-(2/ 3)* (z)^(3/ 2)],(2)^(7/ 2)* Pi]* Integrate[Divide[(t)^(- 1/ 2)* Exp[-(2/ 3)* (t)^(3/ 2)]*AiryAi[t],(z)^(3/ 2)+ (t)^(3/ 2)], {t, 0, Infinity}]	Failure	Failure	Skip	Error
9.10.E20	${\displaystyle{\displaystyle\int_{0}^{x}\!\!\int_{0}^{v}\mathrm{Ai}\left(t\right)\mathrm{d}t\mathrm{d}v=x\int_{0}^{x}\mathrm{Ai}\left(t\right)\mathrm{d}t-\mathrm{Ai}'\left(x\right)+\mathrm{Ai}'\left(0\right)}}$	int(int(AiryAi(t), t = 0..v), v = 0..x)= x*int(AiryAi(t), t = 0..x)- subs( temp=x, diff( AiryAi(temp), temp$(1) ) )+ subs( temp=0, diff( AiryAi(temp), temp$(1) ) )	Integrate[Integrate[AiryAi[t], {t, 0, v}], {v, 0, x}]= x*Integrate[AiryAi[t], {t, 0, x}]- (D[AiryAi[temp], {temp, 1}]/.temp-> x)+ (D[AiryAi[temp], {temp, 1}]/.temp-> 0)	Failure	Failure	Skip	Successful
9.10.E21	${\displaystyle{\displaystyle\int_{0}^{x}\!\!\int_{0}^{v}\mathrm{Bi}\left(t\right)\mathrm{d}t\mathrm{d}v=x\int_{0}^{x}\mathrm{Bi}\left(t\right)\mathrm{d}t-\mathrm{Bi}'\left(x\right)+\mathrm{Bi}'\left(0\right)}}$	int(int(AiryBi(t), t = 0..v), v = 0..x)= x*int(AiryBi(t), t = 0..x)- subs( temp=x, diff( AiryBi(temp), temp$(1) ) )+ subs( temp=0, diff( AiryBi(temp), temp$(1) ) )	Integrate[Integrate[AiryBi[t], {t, 0, v}], {v, 0, x}]= x*Integrate[AiryBi[t], {t, 0, x}]- (D[AiryBi[temp], {temp, 1}]/.temp-> x)+ (D[AiryBi[temp], {temp, 1}]/.temp-> 0)	Failure	Failure	Skip	Successful
9.11.E1	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{3}w}{{\mathrm{d}z}^{3}}-4z\frac{\mathrm{d}w}{\mathrm{d}z}-2w=0}}$	diff(w, [z$(3)])- 4*z*diff(w, z)- 2*w = 0	D[w, {z, 3}]- 4*z*D[w, z]- 2*w = 0	Failure	Failure	Skip	Error
9.11.E2	${\displaystyle{\displaystyle\mathscr{W}\left\{{\mathrm{Ai}^{2}}\left(z\right),\mathrm{Ai}\left(z\right)\mathrm{Bi}\left(z\right),{\mathrm{Bi}^{2}}\left(z\right)\right\}=2\pi^{-3}}}$	((AiryAi(z))^(2))*diff(AiryAi(z)*AiryBi(z)*(AiryBi(z))^(2), z)-diff((AiryAi(z))^(2), z)*(AiryAi(z)*AiryBi(z)*(AiryBi(z))^(2))= 2*(Pi)^(- 3)	Wronskian[{(AiryAi[z])^(2), AiryAi[z]*AiryBi[z]*(AiryBi[z])^(2)}, z]= 2*(Pi)^(- 3)	Failure	Failure	Fail -.6004096260e-1-.6097999473e-2*I <- {z = 2^(1/2)+I*2^(1/2)} -.6004096260e-1+.6097999473e-2*I <- {z = 2^(1/2)-I*2^(1/2)} -21.32909363+6.905982746*I <- {z = -2^(1/2)-I*2^(1/2)} -21.32909363-6.905982746*I <- {z = -2^(1/2)+I*2^(1/2)}	Fail Complex[-0.060040962617560416, -0.006097999474625239] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-0.060040962617560416, 0.006097999474625239] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-21.329093714189053, 6.905982810760452] <- {Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-21.329093714189053, -6.905982810760452] <- {Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.11.E3	${\displaystyle{\displaystyle{\mathrm{Ai}^{2}}\left(x\right)=\frac{1}{4\pi\sqrt{3}}\int_{0}^{\infty}J_{0}\left(\tfrac{1}{12}t^{3}+xt\right)t\mathrm{d}t}}$	(AiryAi(x))^(2)=(1)/(4*Pi*sqrt(3))*int(BesselJ(0, (1)/(12)*(t)^(3)+ x*t)*t, t = 0..infinity)	(AiryAi[x])^(2)=Divide[1,4*Pi*Sqrt[3]]*Integrate[BesselJ[0, Divide[1,12]*(t)^(3)+ x*t]*t, {t, 0, Infinity}]	Failure	Failure	Skip	Skip
9.11.E4	${\displaystyle{\displaystyle{\mathrm{Ai}^{2}}\left(z\right)+{\mathrm{Bi}^{2}}\left(z\right)=\frac{1}{\pi^{3/2}}\int_{0}^{\infty}\exp\left(zt-\tfrac{1}{12}t^{3}\right)t^{-1/2}\mathrm{d}t}}$	(AiryAi(z))^(2)+ (AiryBi(z))^(2)=(1)/((Pi)^(3/ 2))*int(exp(z*t -(1)/(12)*(t)^(3))*(t)^(- 1/ 2), t = 0..infinity)	(AiryAi[z])^(2)+ (AiryBi[z])^(2)=Divide[1,(Pi)^(3/ 2)]*Integrate[Exp[z*t -Divide[1,12]*(t)^(3)]*(t)^(- 1/ 2), {t, 0, Infinity}]	Failure	Failure	Skip	Successful
9.11.E12	${\displaystyle{\displaystyle\int\frac{\mathrm{d}z}{{\mathrm{Ai}^{2}}\left(z\right)}=\pi\frac{\mathrm{Bi}\left(z\right)}{\mathrm{Ai}\left(z\right)}}}$	int((1)/((AiryAi(z))^(2)), z)= Pi*(AiryBi(z))/(AiryAi(z))	Integrate[Divide[1,(AiryAi[z])^(2)], z]= Pi*Divide[AiryBi[z],AiryAi[z]]	Failure	Successful	Skip	-
9.11.E13	${\displaystyle{\displaystyle\int\frac{\mathrm{d}z}{\mathrm{Ai}\left(z\right)\mathrm{Bi}\left(z\right)}=\pi\ln\left(\frac{\mathrm{Bi}\left(z\right)}{\mathrm{Ai}\left(z\right)}\right)}}$	int((1)/(AiryAi(z)*AiryBi(z)), z)= Pi*ln((AiryBi(z))/(AiryAi(z)))	Integrate[Divide[1,AiryAi[z]*AiryBi[z]], z]= Pi*Log[Divide[AiryBi[z],AiryAi[z]]]	Failure	Failure	Skip	Successful
9.11.E14	${\displaystyle{\displaystyle\int\frac{\mathrm{Ai}\left(z\right)\mathrm{Bi}\left(z\right)}{\left({\mathrm{Ai}^{2}}\left(z\right)+{\mathrm{Bi}^{2}}\left(z\right)\right)^{2}}\mathrm{d}z=\frac{\pi}{2}\frac{{\mathrm{Bi}^{2}}\left(z\right)}{{\mathrm{Ai}^{2}}\left(z\right)+{\mathrm{Bi}^{2}}\left(z\right)}}}$	int((AiryAi(z)*AiryBi(z))/(((AiryAi(z))^(2)+ (AiryBi(z))^(2))^(2)), z)=(Pi)/(2)*((AiryBi(z))^(2))/((AiryAi(z))^(2)+ (AiryBi(z))^(2))	Integrate[Divide[AiryAi[z]*AiryBi[z],((AiryAi[z])^(2)+ (AiryBi[z])^(2))^(2)], z]=Divide[Pi,2]*Divide[(AiryBi[z])^(2),(AiryAi[z])^(2)+ (AiryBi[z])^(2)]	Failure	Failure	Skip	Successful
9.11.E15	${\displaystyle{\displaystyle\int_{0}^{\infty}t^{\alpha-1}{\mathrm{Ai}^{2}}\left(t\right)\mathrm{d}t=\frac{2\Gamma\left(\alpha\right)}{\pi^{1/2}12^{(2\alpha+5)/6}\Gamma\left(\frac{1}{3}\alpha+\frac{5}{6}\right)}}}$	int((t)^(alpha - 1)* (AiryAi(t))^(2), t = 0..infinity)=(2*GAMMA(alpha))/((Pi)^(1/ 2)* (12)^((2*alpha + 5)/ 6)* GAMMA((1)/(3)*alpha +(5)/(6)))	Integrate[(t)^(\[Alpha]- 1)* (AiryAi[t])^(2), {t, 0, Infinity}]=Divide[2*Gamma[\[Alpha]],(Pi)^(1/ 2)* (12)^((2*\[Alpha]+ 5)/ 6)* Gamma[Divide[1,3]*\[Alpha]+Divide[5,6]]]	Failure	Failure	Skip	Successful
9.11.E16	${\displaystyle{\displaystyle\int_{-\infty}^{\infty}{\mathrm{Ai}^{3}}\left(t\right)\mathrm{d}t=\frac{{\Gamma^{2}}\left(\frac{1}{3}\right)}{4\pi^{2}}}}$	int((AiryAi(t))^(3), t = - infinity..infinity)=((GAMMA((1)/(3)))^(2))/(4*(Pi)^(2))	Integrate[(AiryAi[t])^(3), {t, - Infinity, Infinity}]=Divide[(Gamma[Divide[1,3]])^(2),4*(Pi)^(2)]	Failure	Failure	Skip	Error
9.11.E17	${\displaystyle{\displaystyle\int_{-\infty}^{\infty}{\mathrm{Ai}^{2}}\left(t\right)\mathrm{Bi}\left(t\right)\mathrm{d}t=\frac{{\Gamma^{2}}\left(\frac{1}{3}\right)}{4\sqrt{3}\pi^{2}}}}$	int((AiryAi(t))^(2)* AiryBi(t), t = - infinity..infinity)=((GAMMA((1)/(3)))^(2))/(4*sqrt(3)*(Pi)^(2))	Integrate[(AiryAi[t])^(2)* AiryBi[t], {t, - Infinity, Infinity}]=Divide[(Gamma[Divide[1,3]])^(2),4*Sqrt[3]*(Pi)^(2)]	Failure	Failure	Skip	Error
9.11.E18	${\displaystyle{\displaystyle\int_{0}^{\infty}{\mathrm{Ai}^{4}}\left(t\right)\mathrm{d}t=\frac{\ln 3}{24\pi^{2}}}}$	int((AiryAi(t))^(4), t = 0..infinity)=(ln(3))/(24*(Pi)^(2))	Integrate[(AiryAi[t])^(4), {t, 0, Infinity}]=Divide[Log[3],24*(Pi)^(2)]	Failure	Failure	Skip	Fail Complex[1.4095755333126005, 1.4142135623730951] <- {Rule[Integrate[Power[AiryAi[t], 4], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[1.4095755333126005, -1.4142135623730951] <- {Rule[Integrate[Power[AiryAi[t], 4], {t, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-1.4188515914335897, -1.4142135623730951] <- {Rule[Integrate[Power[AiryAi[t], 4], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-1.4188515914335897, 1.4142135623730951] <- {Rule[Integrate[Power[AiryAi[t], 4], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.11.E19	${\displaystyle{\displaystyle\int_{0}^{\infty}\frac{\mathrm{d}t}{{\mathrm{Ai}^{2}}\left(t\right)+{\mathrm{Bi}^{2}}\left(t\right)}=\int_{0}^{\infty}\frac{t\mathrm{d}t}{{\mathrm{Ai}'^{2}}\left(t\right)+{\mathrm{Bi}'^{2}}\left(t\right)}}}$	int((1)/((AiryAi(t))^(2)+ (AiryBi(t))^(2)), t = 0..infinity)= int((t)/((subs( temp=t, diff( AiryAi(temp), temp$(1) ) ))^(2)+ (subs( temp=t, diff( AiryBi(temp), temp$(1) ) ))^(2)), t = 0..infinity)	Integrate[Divide[1,(AiryAi[t])^(2)+ (AiryBi[t])^(2)], {t, 0, Infinity}]= Integrate[Divide[t,((D[AiryAi[temp], {temp, 1}]/.temp-> t))^(2)+ ((D[AiryBi[temp], {temp, 1}]/.temp-> t))^(2)], {t, 0, Infinity}]	Failure	Failure	Skip	Error
9.11.E19	${\displaystyle{\displaystyle\int_{0}^{\infty}\frac{t\mathrm{d}t}{{\mathrm{Ai}'^{2}}\left(t\right)+{\mathrm{Bi}'^{2}}\left(t\right)}=\frac{\pi^{2}}{6}}}$	int((t)/((subs( temp=t, diff( AiryAi(temp), temp$(1) ) ))^(2)+ (subs( temp=t, diff( AiryBi(temp), temp$(1) ) ))^(2)), t = 0..infinity)=((Pi)^(2))/(6)	Integrate[Divide[t,((D[AiryAi[temp], {temp, 1}]/.temp-> t))^(2)+ ((D[AiryBi[temp], {temp, 1}]/.temp-> t))^(2)], {t, 0, Infinity}]=Divide[(Pi)^(2),6]	Failure	Failure	Skip	Fail Complex[-0.23072050447513104, 1.4142135623730951] <- {Rule[Integrate[Times[t, Power[Plus[Power[AiryAiPrime[t], 2], Power[AiryBiPrime[t], 2]], -1]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-0.23072050447513104, -1.4142135623730951] <- {Rule[Integrate[Times[t, Power[Plus[Power[AiryAiPrime[t], 2], Power[AiryBiPrime[t], 2]], -1]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[-3.0591476292213216, -1.4142135623730951] <- {Rule[Integrate[Times[t, Power[Plus[Power[AiryAiPrime[t], 2], Power[AiryBiPrime[t], 2]], -1]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[-3.0591476292213216, 1.4142135623730951] <- {Rule[Integrate[Times[t, Power[Plus[Power[AiryAiPrime[t], 2], Power[AiryBiPrime[t], 2]], -1]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
9.12.E1	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}-zw=\frac{1}{\pi}}}$	diff(w, [z$(2)])- z*w =(1)/(Pi)	D[w, {z, 2}]- z*w =Divide[1,Pi]	Failure	Failure	Fail -.3183098861-3.999999998*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)} -4.318309884-0.*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)} -.3183098861+3.999999998*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)} 3.681690112-0.*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)} ... skip entries to safe data	Error
9.12.E4	${\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)=\mathrm{Bi}\left(z\right)\int_{z}^{\infty}\mathrm{Ai}\left(t\right)\mathrm{d}t+\mathrm{Ai}\left(z\right)\int_{0}^{z}\mathrm{Bi}\left(t\right)\mathrm{d}t}}$	AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))= AiryBi(z)*int(AiryAi(t), t = z..infinity)+ AiryAi(z)*int(AiryBi(t), t = 0..z)	ScorerGi[z]= AiryBi[z]*Integrate[AiryAi[t], {t, z, Infinity}]+ AiryAi[z]*Integrate[AiryBi[t], {t, 0, z}]	Successful	Failure	-	Successful
9.12.E5	${\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)=\mathrm{Bi}\left(z\right)\int_{-\infty}^{z}\mathrm{Ai}\left(t\right)\mathrm{d}t-\mathrm{Ai}\left(z\right)\int_{-\infty}^{z}\mathrm{Bi}\left(t\right)\mathrm{d}t}}$	AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))= AiryBi(z)*int(AiryAi(t), t = - infinity..z)- AiryAi(z)*int(AiryBi(t), t = - infinity..z)	ScorerHi[z]= AiryBi[z]*Integrate[AiryAi[t], {t, - Infinity, z}]- AiryAi[z]*Integrate[AiryBi[t], {t, - Infinity, z}]	Successful	Failure	-	Skip
9.12.E6	${\displaystyle{\displaystyle\mathrm{Gi}\left(0\right)=\tfrac{1}{2}\mathrm{Hi}\left(0\right)}}$	AiryBi(0)*(int(AiryAi(t), t = (0) .. infinity))+AiryAi(0)*(int(AiryBi(t), t = 0 .. (0)))=(1)/(2)*AiryBi(0)*(int(AiryAi(t), t = -infinity .. (0)))-AiryAi(0)*(int(AiryBi(t), t = -infinity .. (0)))	ScorerGi[0]=Divide[1,2]*ScorerHi[0]	Successful	Successful	-	-
9.12.E6	${\displaystyle{\displaystyle\tfrac{1}{2}\mathrm{Hi}\left(0\right)=\tfrac{1}{3}\mathrm{Bi}\left(0\right)}}$	(1)/(2)*AiryBi(0)*(int(AiryAi(t), t = -infinity .. (0)))-AiryAi(0)*(int(AiryBi(t), t = -infinity .. (0)))=(1)/(3)*AiryBi(0)	Divide[1,2]*ScorerHi[0]=Divide[1,3]*AiryBi[0]	Successful	Successful	-	-
9.12.E7	${\displaystyle{\displaystyle\mathrm{Gi}'\left(0\right)=\tfrac{1}{2}\mathrm{Hi}'\left(0\right)}}$	subs( temp=0, diff( AiryBi(temp)*(int(AiryAi(t), t = (temp) .. infinity))+AiryAi(temp)*(int(AiryBi(t), t = 0 .. (temp))), temp$(1) ) )=(1)/(2)*subs( temp=0, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) )	(D[ScorerGi[temp], {temp, 1}]/.temp-> 0)=Divide[1,2]*(D[ScorerHi[temp], {temp, 1}]/.temp-> 0)	Successful	Successful	-	-
9.12.E7	${\displaystyle{\displaystyle\tfrac{1}{2}\mathrm{Hi}'\left(0\right)=\tfrac{1}{3}\mathrm{Bi}'\left(0\right)}}$	(1)/(2)*subs( temp=0, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) )=(1)/(3)*subs( temp=0, diff( AiryBi(temp), temp$(1) ) )	Divide[1,2]*(D[ScorerHi[temp], {temp, 1}]/.temp-> 0)=Divide[1,3]*(D[AiryBi[temp], {temp, 1}]/.temp-> 0)	Successful	Successful	-	-
9.12.E7	${\displaystyle{\displaystyle\tfrac{1}{3}\mathrm{Bi}'\left(0\right)=1\Big{/}\left(3^{5/6}\Gamma\left(\tfrac{1}{3}\right)\right)}}$	(1)/(3)*subs( temp=0, diff( AiryBi(temp), temp$(1) ) )= 1/((3)^(5/ 6)* GAMMA((1)/(3)))	Divide[1,3]*(D[AiryBi[temp], {temp, 1}]/.temp-> 0)= 1/((3)^(5/ 6)* Gamma[Divide[1,3]])	Successful	Successful	-	-
9.12.E11	${\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)+\mathrm{Hi}\left(z\right)=\mathrm{Bi}\left(z\right)}}$	AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))+ AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))= AiryBi(z)	ScorerGi[z]+ ScorerHi[z]= AiryBi[z]	Successful	Successful	-	-
9.12.E12	${\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)=\tfrac{1}{2}e^{\pi i/3}\mathrm{Hi}\left(ze^{-2\pi i/3}\right)+\tfrac{1}{2}e^{-\pi i/3}\mathrm{Hi}\left(ze^{2\pi i/3}\right)}}$	AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))=(1)/(2)*exp(Pi*I/ 3)*AiryBi(z*exp(- 2*Pi*I/ 3))*(int(AiryAi(t), t = -infinity .. (z*exp(- 2*Pi*I/ 3))))-AiryAi(z*exp(- 2*Pi*I/ 3))*(int(AiryBi(t), t = -infinity .. (z*exp(- 2*Pi*I/ 3))))+(1)/(2)*exp(- Pi*I/ 3)*AiryBi(z*exp(2*Pi*I/ 3))*(int(AiryAi(t), t = -infinity .. (z*exp(2*Pi*I/ 3))))-AiryAi(z*exp(2*Pi*I/ 3))*(int(AiryBi(t), t = -infinity .. (z*exp(2*Pi*I/ 3))))	ScorerGi[z]=Divide[1,2]*Exp[Pi*I/ 3]*ScorerHi[z*Exp[- 2*Pi*I/ 3]]+Divide[1,2]*Exp[- Pi*I/ 3]*ScorerHi[z*Exp[2*Pi*I/ 3]]	Failure	Successful	Fail .6194989342-.2058648052*I <- {z = 2^(1/2)+I*2^(1/2)} .6194989342+.2058648052*I <- {z = 2^(1/2)-I*2^(1/2)} 1.652883055+1.203317832*I <- {z = -2^(1/2)-I*2^(1/2)} 1.652883056-1.203317832*I <- {z = -2^(1/2)+I*2^(1/2)}	-
9.12.E13	${\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)=e^{-\pi i/3}\mathrm{Hi}\left(ze^{+2\pi i/3}\right)+i\mathrm{Ai}\left(z\right)}}$	AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))= exp(- Pi*I/ 3)*AiryBi(z*exp(+ 2*Pi*I/ 3))*(int(AiryAi(t), t = -infinity .. (z*exp(+ 2*Pi*I/ 3))))-AiryAi(z*exp(+ 2*Pi*I/ 3))*(int(AiryBi(t), t = -infinity .. (z*exp(+ 2*Pi*I/ 3))))+ I*AiryAi(z)	ScorerGi[z]= Exp[- Pi*I/ 3]*ScorerHi[z*Exp[+ 2*Pi*I/ 3]]+ I*AiryAi[z]	Failure	Successful	Fail .1301354555-.9994650010e-1*I <- {z = 2^(1/2)+I*2^(1/2)} .5221313133+.4008588212*I <- {z = 2^(1/2)-I*2^(1/2)} .340645583e-1+.100353266*I <- {z = -2^(1/2)-I*2^(1/2)} 2.243678175-.228349494*I <- {z = -2^(1/2)+I*2^(1/2)}	-
9.12.E13	${\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)=e^{+\pi i/3}\mathrm{Hi}\left(ze^{-2\pi i/3}\right)-i\mathrm{Ai}\left(z\right)}}$	AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))= exp(+ Pi*I/ 3)*AiryBi(z*exp(- 2*Pi*I/ 3))*(int(AiryAi(t), t = -infinity .. (z*exp(- 2*Pi*I/ 3))))-AiryAi(z*exp(- 2*Pi*I/ 3))*(int(AiryBi(t), t = -infinity .. (z*exp(- 2*Pi*I/ 3))))- I*AiryAi(z)	ScorerGi[z]= Exp[+ Pi*I/ 3]*ScorerHi[z*Exp[- 2*Pi*I/ 3]]- I*AiryAi[z]	Failure	Successful	Fail .5221313133-.4008588212*I <- {z = 2^(1/2)+I*2^(1/2)} .1301354555+.9994650010e-1*I <- {z = 2^(1/2)-I*2^(1/2)} 2.243678175+.228349494*I <- {z = -2^(1/2)-I*2^(1/2)} .340645583e-1-.100353266*I <- {z = -2^(1/2)+I*2^(1/2)}	-
9.12.E14	${\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)=e^{+2\pi i/3}\mathrm{Hi}\left(ze^{+2\pi i/3}\right)+2e^{-\pi i/6}\mathrm{Ai}\left(ze^{-2\pi i/3}\right)}}$	AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))= exp(+ 2*Pi*I/ 3)*AiryBi(z*exp(+ 2*Pi*I/ 3))*(int(AiryAi(t), t = -infinity .. (z*exp(+ 2*Pi*I/ 3))))-AiryAi(z*exp(+ 2*Pi*I/ 3))*(int(AiryBi(t), t = -infinity .. (z*exp(+ 2*Pi*I/ 3))))+ 2*exp(- Pi*I/ 6)*AiryAi(z*exp(- 2*Pi*I/ 3))	ScorerHi[z]= Exp[+ 2*Pi*I/ 3]*ScorerHi[z*Exp[+ 2*Pi*I/ 3]]+ 2*Exp[- Pi*I/ 6]*AiryAi[z*Exp[- 2*Pi*I/ 3]]	Failure	Successful	Fail -.1731124148-.2254012203*I <- {z = 2^(1/2)+I*2^(1/2)} .6943078446-.9043579630*I <- {z = 2^(1/2)-I*2^(1/2)} .1738169473-.59001540e-1*I <- {z = -2^(1/2)-I*2^(1/2)} -.3955129264-3.886164592*I <- {z = -2^(1/2)+I*2^(1/2)}	-
9.12.E14	${\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)=e^{-2\pi i/3}\mathrm{Hi}\left(ze^{-2\pi i/3}\right)+2e^{+\pi i/6}\mathrm{Ai}\left(ze^{+2\pi i/3}\right)}}$	AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))= exp(- 2*Pi*I/ 3)*AiryBi(z*exp(- 2*Pi*I/ 3))*(int(AiryAi(t), t = -infinity .. (z*exp(- 2*Pi*I/ 3))))-AiryAi(z*exp(- 2*Pi*I/ 3))*(int(AiryBi(t), t = -infinity .. (z*exp(- 2*Pi*I/ 3))))+ 2*exp(+ Pi*I/ 6)*AiryAi(z*exp(+ 2*Pi*I/ 3))	ScorerHi[z]= Exp[- 2*Pi*I/ 3]*ScorerHi[z*Exp[- 2*Pi*I/ 3]]+ 2*Exp[+ Pi*I/ 6]*AiryAi[z*Exp[+ 2*Pi*I/ 3]]	Failure	Successful	Fail .6943078446+.9043579630*I <- {z = 2^(1/2)+I*2^(1/2)} -.1731124148+.2254012203*I <- {z = 2^(1/2)-I*2^(1/2)} -.3955129264+3.886164592*I <- {z = -2^(1/2)-I*2^(1/2)} .1738169473+.59001540e-1*I <- {z = -2^(1/2)+I*2^(1/2)}	-
9.12.E15	${\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)=\frac{3^{-2/3}}{\pi}\*\sum_{k=0}^{\infty}\cos\left(\frac{2k-1}{3}\pi\right)\Gamma\left(\frac{k+1}{3}\right)\frac{(3^{1/3}z)^{k}}{k!}}}$	AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))=((3)^(- 2/ 3))/(Pi)* sum(cos((2*k - 1)/(3)*Pi)*GAMMA((k + 1)/(3))*(((3)^(1/ 3)* z)^(k))/(factorial(k)), k = 0..infinity)	ScorerGi[z]=Divide[(3)^(- 2/ 3),Pi]* Sum[Cos[Divide[2*k - 1,3]*Pi]*Gamma[Divide[k + 1,3]]*Divide[((3)^(1/ 3)* z)^(k),(k)!], {k, 0, Infinity}]	Failure	Successful	Skip	-
9.12.E16	${\displaystyle{\displaystyle\mathrm{Gi}'\left(z\right)=\frac{3^{-1/3}}{\pi}\*\sum_{k=0}^{\infty}\cos\left(\frac{2k+1}{3}\pi\right)\Gamma\left(\frac{k+2}{3}\right)\frac{(3^{1/3}z)^{k}}{k!}}}$	subs( temp=z, diff( AiryBi(temp)*(int(AiryAi(t), t = (temp) .. infinity))+AiryAi(temp)*(int(AiryBi(t), t = 0 .. (temp))), temp$(1) ) )=((3)^(- 1/ 3))/(Pi)* sum(cos((2*k + 1)/(3)*Pi)*GAMMA((k + 2)/(3))*(((3)^(1/ 3)* z)^(k))/(factorial(k)), k = 0..infinity)	(D[ScorerGi[temp], {temp, 1}]/.temp-> z)=Divide[(3)^(- 1/ 3),Pi]* Sum[Cos[Divide[2*k + 1,3]*Pi]*Gamma[Divide[k + 2,3]]*Divide[((3)^(1/ 3)* z)^(k),(k)!], {k, 0, Infinity}]	Failure	Successful	Skip	-
9.12.E17	${\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)=\frac{3^{-2/3}}{\pi}\sum_{k=0}^{\infty}\Gamma\left(\frac{k+1}{3}\right)\frac{(3^{1/3}z)^{k}}{k!}}}$	AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))=((3)^(- 2/ 3))/(Pi)*sum(GAMMA((k + 1)/(3))*(((3)^(1/ 3)* z)^(k))/(factorial(k)), k = 0..infinity)	ScorerHi[z]=Divide[(3)^(- 2/ 3),Pi]*Sum[Gamma[Divide[k + 1,3]]*Divide[((3)^(1/ 3)* z)^(k),(k)!], {k, 0, Infinity}]	Failure	Successful	Skip	-
9.12.E18	${\displaystyle{\displaystyle\mathrm{Hi}'\left(z\right)=\frac{3^{-1/3}}{\pi}\sum_{k=0}^{\infty}\Gamma\left(\frac{k+2}{3}\right)\frac{(3^{1/3}z)^{k}}{k!}}}$	subs( temp=z, diff( AiryBi(temp)*(int(AiryAi(t), t = -infinity .. (temp)))-AiryAi(temp)*(int(AiryBi(t), t = -infinity .. (temp))), temp$(1) ) )=((3)^(- 1/ 3))/(Pi)*sum(GAMMA((k + 2)/(3))*(((3)^(1/ 3)* z)^(k))/(factorial(k)), k = 0..infinity)	(D[ScorerHi[temp], {temp, 1}]/.temp-> z)=Divide[(3)^(- 1/ 3),Pi]*Sum[Gamma[Divide[k + 2,3]]*Divide[((3)^(1/ 3)* z)^(k),(k)!], {k, 0, Infinity}]	Failure	Successful	Skip	-
9.12.E19	${\displaystyle{\displaystyle\mathrm{Gi}\left(x\right)=\frac{1}{\pi}\int_{0}^{\infty}\sin\left(\tfrac{1}{3}t^{3}+xt\right)\mathrm{d}t}}$	AiryBi(x)*(int(AiryAi(t), t = (x) .. infinity))+AiryAi(x)*(int(AiryBi(t), t = 0 .. (x)))=(1)/(Pi)*int(sin((1)/(3)*(t)^(3)+ x*t), t = 0..infinity)	ScorerGi[x]=Divide[1,Pi]*Integrate[Sin[Divide[1,3]*(t)^(3)+ x*t], {t, 0, Infinity}]	Failure	Failure	Skip	Successful
9.12.E20	${\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)=\frac{1}{\pi}\int_{0}^{\infty}\exp\left(-\tfrac{1}{3}t^{3}+zt\right)\mathrm{d}t}}$	AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))=(1)/(Pi)*int(exp(-(1)/(3)*(t)^(3)+ z*t), t = 0..infinity)	ScorerHi[z]=Divide[1,Pi]*Integrate[Exp[-Divide[1,3]*(t)^(3)+ z*t], {t, 0, Infinity}]	Failure	Failure	Skip	Successful
9.12.E21	${\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)=-\frac{1}{\pi}\int_{0}^{\infty}\exp\left(-\tfrac{1}{3}t^{3}-\tfrac{1}{2}zt\right)\cos\left(\tfrac{1}{2}\sqrt{3}zt+\tfrac{2}{3}\pi\right)\mathrm{d}t}}$	AiryBi(z)*(int(AiryAi(t), t = (z) .. infinity))+AiryAi(z)*(int(AiryBi(t), t = 0 .. (z)))= -(1)/(Pi)*int(exp(-(1)/(3)*(t)^(3)-(1)/(2)*z*t)*cos((1)/(2)*sqrt(3)*z*t +(2)/(3)*Pi), t = 0..infinity)	ScorerGi[z]= -Divide[1,Pi]*Integrate[Exp[-Divide[1,3]*(t)^(3)-Divide[1,2]*z*t]*Cos[Divide[1,2]*Sqrt[3]*z*t +Divide[2,3]*Pi], {t, 0, Infinity}]	Failure	Failure	Skip	Error
9.12.E22	${\displaystyle{\displaystyle\mathrm{Hi}\left(-z\right)=\frac{4z^{2}}{3^{3/2}\pi^{2}}\int_{0}^{\infty}\frac{K_{1/3}\left(t\right)}{\zeta^{2}+t^{2}}\mathrm{d}t}}$	AiryBi(- z)*(int(AiryAi(t), t = -infinity .. (- z)))-AiryAi(- z)*(int(AiryBi(t), t = -infinity .. (- z)))=(4*(z)^(2))/((3)^(3/ 2)* (Pi)^(2))*int((BesselK(1/ 3, t))/((2)/(3)*((z)^((3)/(2)))^(2)+ (t)^(2)), t = 0..infinity)	ScorerHi[- z]=Divide[4*(z)^(2),(3)^(3/ 2)* (Pi)^(2)]*Integrate[Divide[BesselK[1/ 3, t],Divide[2,3]*((z)^(Divide[3,2]))^(2)+ (t)^(2)], {t, 0, Infinity}]	Failure	Failure	Skip	Fail Complex[0.04337928599820519, -0.02597020526100885] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[0.04337928599820519, 0.02597020526100885] <- {Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
9.12.E24	${\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)=\frac{3^{-2/3}}{2\pi^{2}i}\int_{-i\infty}^{i\infty}\Gamma\left(\tfrac{1}{3}+\tfrac{1}{3}t\right)\Gamma\left(-t\right)(3^{1/3}e^{\pi i}z)^{t}\mathrm{d}t}}$	AiryBi(z)*(int(AiryAi(t), t = -infinity .. (z)))-AiryAi(z)*(int(AiryBi(t), t = -infinity .. (z)))=((3)^(- 2/ 3))/(2*(Pi)^(2)* I)*int(GAMMA((1)/(3)+(1)/(3)*t)*GAMMA(- t)*((3)^(1/ 3)* exp(Pi*I)*z)^(t), t = - I*infinity..I*infinity)	ScorerHi[z]=Divide[(3)^(- 2/ 3),2*(Pi)^(2)* I]*Integrate[Gamma[Divide[1,3]+Divide[1,3]*t]*Gamma[- t]*((3)^(1/ 3)* Exp[Pi*I]*z)^(t), {t, - I*Infinity, I*Infinity}]	Failure	Failure	Skip	Error
9.13.E13	${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}t}^{2}}=\tfrac{1}{4}m^{2}t^{m-2}w}}$	diff(w, [t$(2)])=(1)/(4)*(m)^(2)* (t)^(m - 2)* w	D[w, {t, 2}]=Divide[1,4]*(m)^(2)* (t)^(m - 2)* w	Failure	Failure	Fail -.2500000000 <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 1} -1.414213562-1.414213562*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 2} -0.-8.999999996*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), m = 3} -0.+.2500000000*I <- {t = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), m = 1} ... skip entries to safe data	Error
9.13.E20	${\displaystyle{\displaystyle U_{1}(x,\alpha)=\frac{1}{(\alpha+2)^{1/(\alpha+2)}}\*\Gamma\left(\frac{\alpha+1}{\alpha+2}\right)x^{1/2}J_{-1/(\alpha+2)}\left(\frac{2}{\alpha+2}x^{(\alpha+2)/2}\right)}}$	U[1]*(x , alpha)=(1)/((alpha + 2)^(1/(alpha + 2)))* GAMMA((alpha + 1)/(alpha + 2))*(x)^(1/ 2)* BesselJ(- 1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/ 2))	Subscript[U, 1]*(x , \[Alpha])=Divide[1,(\[Alpha]+ 2)^(1/(\[Alpha]+ 2))]* Gamma[Divide[\[Alpha]+ 1,\[Alpha]+ 2]]*(x)^(1/ 2)* BesselJ[- 1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/ 2)]	Failure	Failure	Error	Error
9.13.E21	${\displaystyle{\displaystyle U_{2}(x,\alpha)=(\alpha+2)^{1/(\alpha+2)}\*\Gamma\left(\frac{\alpha+3}{\alpha+2}\right)x^{1/2}J_{1/(\alpha+2)}\left(\frac{2}{\alpha+2}x^{(\alpha+2)/2}\right)}}$	U[2]*(x , alpha)=(alpha + 2)^(1/(alpha + 2))* GAMMA((alpha + 3)/(alpha + 2))*(x)^(1/ 2)* BesselJ(1/(alpha + 2), (2)/(alpha + 2)*(x)^((alpha + 2)/ 2))	Subscript[U, 2]*(x , \[Alpha])=(\[Alpha]+ 2)^(1/(\[Alpha]+ 2))* Gamma[Divide[\[Alpha]+ 3,\[Alpha]+ 2]]*(x)^(1/ 2)* BesselJ[1/(\[Alpha]+ 2), Divide[2,\[Alpha]+ 2]*(x)^((\[Alpha]+ 2)/ 2)]	Failure	Failure	Error	Error
9.13.E23	${\displaystyle{\displaystyle U_{1}(x,\alpha)=\frac{\pi^{1/2}}{2^{(m+2)/(2m)}\Gamma\left(1/m\right)}\left(W_{m}(t)+W_{m}(-t)\right)}}$	U[1]*(x , alpha)=((Pi)^(1/ 2))/((2)^((m + 2)/(2*m))* GAMMA(1/ m))*(W[m]*(t)+ W[m]*(- t))	Subscript[U, 1]*(x , \[Alpha])=Divide[(Pi)^(1/ 2),(2)^((m + 2)/(2*m))* Gamma[1/ m]]*(Subscript[W, m]*(t)+ Subscript[W, m]*(- t))	Failure	Failure	Error	Error
9.13.E24	${\displaystyle{\displaystyle U_{2}(x,\alpha)=\frac{\pi^{1/2}m^{2/m}}{2^{(m+2)/(2m)}\Gamma\left(-1/m\right)}\left(W_{m}(t){-}W_{m}(-t)\right)}}$	U[2]*(x , alpha)=((Pi)^(1/ 2)* (m)^(2/ m))/((2)^((m + 2)/(2*m))* GAMMA(- 1/ m))*(W[m]*(t)- W[m]*(- t))	Subscript[U, 2]*(x , \[Alpha])=Divide[(Pi)^(1/ 2)* (m)^(2/ m),(2)^((m + 2)/(2*m))* Gamma[- 1/ m]]*(Subscript[W, m]*(t)- Subscript[W, m]*(- t))	Failure	Failure	Skip	Error