# Results of Painlevé Transcendents

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DLMF Formula Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
32.2.E1 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=6w^{2}% +z}}$ diff(w, [z$(2)])= 6*(w)^(2)+ z D[w, {z, 2}]= 6*(w)^(2)+ z Failure Failure Fail -1.414213562-25.41421355*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)} -1.414213562-22.58578643*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)} 1.414213562-22.58578643*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)} 1.414213562-25.41421355*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)} ... skip entries to safe data Fail Complex[-1.4142135623730951, -25.414213562373096] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]} Complex[-1.4142135623730951, -22.585786437626904] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]} Complex[1.4142135623730951, -22.585786437626904] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]} Complex[1.4142135623730951, -25.414213562373096] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} ... skip entries to safe data 32.2.E2 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=2w^{3}% +zw+\alpha}}$ diff(w, [z$(2)])= 2*(w)^(3)+ z*w + alpha D[w, {z, 2}]= 2*(w)^(3)+ z*w + \[Alpha] Failure Failure
Fail
9.899494928-16.72792205*I <- {alpha = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
5.899494930-12.72792205*I <- {alpha = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
9.899494928-8.727922054*I <- {alpha = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
13.89949493-12.72792205*I <- {alpha = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[9.899494936611665, -16.72792206135786] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.899494936611665, -13.899494936611665] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[12.727922061357857, -13.899494936611665] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[12.727922061357857, -16.72792206135786] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
32.2.E3 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=\frac{% 1}{w}\left(\frac{\mathrm{d}w}{\mathrm{d}z}\right)^{2}-\frac{1}{z}\frac{\mathrm% {d}w}{\mathrm{d}z}+\frac{\alpha w^{2}+\beta}{z}+\gamma w^{3}+\frac{\delta}{w}}}$ diff(w, [z$(2)])=(1)/(w)*(diff(w, z))^(2)-(1)/(z)*diff(w, z)+(alpha*(w)^(2)+ beta)/(z)+ gamma*(w)^(3)+(delta)/(w) D[w, {z, 2}]=Divide[1,w]*(D[w, z])^(2)-Divide[1,z]*D[w, z]+Divide[\[Alpha]*(w)^(2)+ \[Beta],z]+ \[Gamma]*(w)^(3)+Divide[\[Delta],w] Failure Failure Skip Skip 32.2.E4 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=\frac{% 1}{2w}\left(\frac{\mathrm{d}w}{\mathrm{d}z}\right)^{2}+\frac{3}{2}w^{3}+4zw^{2% }+2(z^{2}-\alpha)w+\frac{\beta}{w}}}$ diff(w, [z$(2)])=(1)/(2*w)*(diff(w, z))^(2)+(3)/(2)*(w)^(3)+ 4*z*(w)^(2)+ 2*((z)^(2)- alpha)* w +(beta)/(w) D[w, {z, 2}]=Divide[1,2*w]*(D[w, z])^(2)+Divide[3,2]*(w)^(3)+ 4*z*(w)^(2)+ 2*((z)^(2)- \[Alpha])* w +Divide[\[Beta],w] Failure Failure
Fail
41.42640684-34.42640684*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
-26.45584410-11.79898986*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-3.82842712+10.82842712*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
18.79898986+33.45584410*I <- {alpha = 2^(1/2)+I*2^(1/2), beta = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[41.42640687119285, -34.42640687119285] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[β, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[42.42640687119285, -33.42640687119285] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[β, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[43.42640687119285, -34.42640687119285] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[β, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[42.42640687119285, -35.42640687119285] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[α, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[β, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
32.2.E5 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=\left(% \frac{1}{2w}+\frac{1}{w-1}\right)\left(\frac{\mathrm{d}w}{\mathrm{d}z}\right)^% {2}-\frac{1}{z}\frac{\mathrm{d}w}{\mathrm{d}z}+\frac{(w-1)^{2}}{z^{2}}\left(% \alpha w+\frac{\beta}{w}\right)+\frac{\gamma w}{z}+\frac{\delta w(w+1)}{w-1}}}$ diff(w, [z$(2)])=((1)/(2*w)+(1)/(w - 1))*(diff(w, z))^(2)-(1)/(z)*diff(w, z)+((w - 1)^(2))/((z)^(2))*(alpha*w +(beta)/(w))+(gamma*w)/(z)+(delta*w*(w + 1))/(w - 1) D[w, {z, 2}]=(Divide[1,2*w]+Divide[1,w - 1])*(D[w, z])^(2)-Divide[1,z]*D[w, z]+Divide[(w - 1)^(2),(z)^(2)]*(\[Alpha]*w +Divide[\[Beta],w])+Divide[\[Gamma]*w,z]+Divide[\[Delta]*w*(w + 1),w - 1] Failure Failure Skip Skip 32.2.E6 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=\frac{% 1}{2}\left(\frac{1}{w}+\frac{1}{w-1}+\frac{1}{w-z}\right)\left(\frac{\mathrm{d% }w}{\mathrm{d}z}\right)^{2}-\left(\frac{1}{z}+\frac{1}{z-1}+\frac{1}{w-z}% \right)\frac{\mathrm{d}w}{\mathrm{d}z}+\frac{w(w-1)(w-z)}{z^{2}(z-1)^{2}}\left% (\alpha+\frac{\beta z}{w^{2}}+\frac{\gamma(z-1)}{(w-1)^{2}}+\frac{\delta z(z-1% )}{(w-z)^{2}}\right)}}$ diff(w, [z$(2)])=(1)/(2)*((1)/(w)+(1)/(w - 1)+(1)/(w - z))*(diff(w, z))^(2)-((1)/(z)+(1)/(z - 1)+(1)/(w - z))* diff(w, z)+(w*(w - 1)*(w - z))/((z)^(2)*(z - 1)^(2))*(alpha +(beta*z)/((w)^(2))+(gamma*(z - 1))/((w - 1)^(2))+(delta*z*(z - 1))/((w - z)^(2))) D[w, {z, 2}]=Divide[1,2]*(Divide[1,w]+Divide[1,w - 1]+Divide[1,w - z])*(D[w, z])^(2)-(Divide[1,z]+Divide[1,z - 1]+Divide[1,w - z])* D[w, z]+Divide[w*(w - 1)*(w - z),(z)^(2)*(z - 1)^(2)]*(\[Alpha]+Divide[\[Beta]*z,(w)^(2)]+Divide[\[Gamma]*(z - 1),(w - 1)^(2)]+Divide[\[Delta]*z*(z - 1),(w - z)^(2)]) Failure Failure Skip Skip
32.2.E7 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=F\left% (z,w,\frac{\mathrm{d}w}{\mathrm{d}z}\right)}}$ diff(w, [z$(2)])= F*(z , w , diff(w, z)) D[w, {z, 2}]= F*(z , w , D[w, z]) Failure Failure Error Error 32.2.E9 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}u}{{\mathrm{d}\zeta}^{2}}=% \frac{1}{u}\left(\frac{\mathrm{d}u}{\mathrm{d}\zeta}\right)^{2}-\frac{1}{\zeta% }\frac{\mathrm{d}u}{\mathrm{d}\zeta}+\frac{u^{2}(\alpha+\gamma u)}{4\zeta^{2}}% +\frac{\beta}{4\zeta}+\frac{\delta}{4u}}}$ diff(u, [zeta$(2)])=(1)/(u)*(diff(u, zeta))^(2)-(1)/(zeta)*diff(u, zeta)+((u)^(2)*(alpha + gamma*u))/(4*(zeta)^(2))+(beta)/(4*zeta)+(delta)/(4*u) D[u, {\[zeta], 2}]=Divide[1,u]*(D[u, \[zeta]])^(2)-Divide[1,\[zeta]]*D[u, \[zeta]]+Divide[(u)^(2)*(\[Alpha]+ \[Gamma]*u),4*(\[zeta])^(2)]+Divide[\[Beta],4*\[zeta]]+Divide[\[Delta],4*u] Failure Failure Skip Error
32.2.E10 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}u}{{\mathrm{d}z}^{2}}+\frac{% 1}{z}\frac{\mathrm{d}u}{\mathrm{d}z}=\frac{2\alpha}{z}\sin u+2\gamma\sin\left(% 2u\right)}}$ diff(u, [z$(2)])+(1)/(z)*diff(u, z)=(2*alpha)/(z)*sin(u)+ 2*gamma*sin(2*u) D[u, {z, 2}]+Divide[1,z]*D[u, z]=Divide[2*\[Alpha],z]*Sin[u]+ 2*\[Gamma]*Sin[2*u] Failure Failure Fail -7.322152505+8.654853973*I <- {alpha = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)} -2.415558484+4.955305834*I <- {alpha = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)} 1.283989655+9.861899855*I <- {alpha = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)} -3.622604366+13.56144799*I <- {alpha = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)} ... skip entries to safe data Skip 32.2.E11 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}u}{{\mathrm{d}\zeta}^{2}}=3u% ^{5}+2\zeta u^{3}+\left(\tfrac{1}{4}\zeta^{2}-\nu-\tfrac{1}{2}\right)u+\frac{% \beta}{32u^{3}}}}$ diff(u, [zeta$(2)])= 3*(u)^(5)+ 2*zeta*(u)^(3)+((1)/(4)*(zeta)^(2)- nu -(1)/(2))* u +(beta)/(32*(u)^(3)) D[u, {\[zeta], 2}]= 3*(u)^(5)+ 2*\[zeta]*(u)^(3)+(Divide[1,4]*(\[zeta])^(2)- \[Nu]-Divide[1,2])* u +Divide[\[Beta],32*(u)^(3)] Failure Failure
Fail
102.0035712+71.18295663*I <- {beta = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)}
67.17514413+42.01138379*I <- {beta = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)}
38.00357129+71.18295663*I <- {beta = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)}
67.17514413+106.0113837*I <- {beta = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
32.2.E12 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}u}{{\mathrm{d}\zeta}^{2}}=-% \frac{\alpha\cosh u}{2(\sinh u)^{3}}-\frac{\beta\sinh u}{2(\cosh u)^{3}}-% \tfrac{1}{4}\gamma e^{\zeta}\sinh\left(2u\right)-\tfrac{1}{8}\delta e^{2\zeta}% \sinh\left(4u\right)}}$ diff(u, [zeta$(2)])= -(alpha*cosh(u))/(2*(sinh(u))^(3))-(beta*sinh(u))/(2*(cosh(u))^(3))-(1)/(4)*gamma*exp(zeta)*sinh(2*u)-(1)/(8)*delta*exp(2*zeta)*sinh(4*u) D[u, {\[zeta], 2}]= -Divide[\[Alpha]*Cosh[u],2*(Sinh[u])^(3)]-Divide[\[Beta]*Sinh[u],2*(Cosh[u])^(3)]-Divide[1,4]*\[Gamma]*Exp[\[zeta]]*Sinh[2*u]-Divide[1,8]*\[Delta]*Exp[2*\[zeta]]*Sinh[4*u] Failure Failure Skip Error 32.2.E13 ${\displaystyle{\displaystyle z(1-z)I\left(\int_{\infty}^{w}\frac{\mathrm{d}t}{% \sqrt{t(t-1)(t-z)}}\right)=\sqrt{w(w-1)(w-z)}\*\left(\alpha+\frac{\beta z}{w^{% 2}}+\frac{\gamma(z-1)}{(w-1)^{2}}+(\delta-\tfrac{1}{2})\frac{z(z-1)}{(w-z)^{2}% }\right)}}$ z*(1 - z)* I*(int((1)/(sqrt(t*(t - 1)*(t - z))), t = infinity..w))=sqrt(w*(w - 1)*(w - z))*(alpha +(beta*z)/((w)^(2))+(gamma*(z - 1))/((w - 1)^(2))+(delta -(1)/(2))*(z*(z - 1))/((w - z)^(2))) z*(1 - z)* I*(Integrate[Divide[1,Sqrt[t*(t - 1)*(t - z)]], {t, Infinity, w}])=Sqrt[w*(w - 1)*(w - z)]*(\[Alpha]+Divide[\[Beta]*z,(w)^(2)]+Divide[\[Gamma]*(z - 1),(w - 1)^(2)]+(\[Delta]-Divide[1,2])*Divide[z*(z - 1),(w - z)^(2)]) Failure Failure Skip Error 32.2.E14 ${\displaystyle{\displaystyle I=z(1-z)\frac{{\mathrm{d}}^{2}}{{\mathrm{d}z}^{2}% }+(1-2z)\frac{\mathrm{d}}{\mathrm{d}z}-\frac{1}{4}}}$ I = z*(1 - z)* diff(+(1 - 2*z)* diff(-, z), [z$(2)])(1)/(4) I = z*(1 - z)* D[+(1 - 2*z)* D[-, z], {z, 2}]Divide[1,4] Error Failure - Error
32.2#Ex3 ${\displaystyle{\displaystyle\frac{\mathrm{d}f_{1}}{\mathrm{d}z}+f_{1}(f_{2}-f_% {3})+2\mu_{1}=0}}$ diff(f[1], z)+ f[1]*(f[2]- f[3])+ 2*mu[1]= 0 D[Subscript[f, 1], z]+ Subscript[f, 1]*(Subscript[f, 2]- Subscript[f, 3])+ 2*Subscript[\[Mu], 1]= 0 Failure Failure
Fail
2.828427124+2.828427124*I <- {f[1] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), f[3] = 2^(1/2)+I*2^(1/2), mu[1] = 2^(1/2)+I*2^(1/2)}
2.828427124-2.828427124*I <- {f[1] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), f[3] = 2^(1/2)+I*2^(1/2), mu[1] = 2^(1/2)-I*2^(1/2)}
-2.828427124-2.828427124*I <- {f[1] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), f[3] = 2^(1/2)+I*2^(1/2), mu[1] = -2^(1/2)-I*2^(1/2)}
-2.828427124+2.828427124*I <- {f[1] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), f[3] = 2^(1/2)+I*2^(1/2), mu[1] = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[μ, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[μ, 1], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[μ, 1], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[μ, 1], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
32.2#Ex4 ${\displaystyle{\displaystyle\frac{\mathrm{d}f_{2}}{\mathrm{d}z}+f_{2}(f_{3}-f_% {1})+2\mu_{2}=0}}$ diff(f[2], z)+ f[2]*(f[3]- f[1])+ 2*mu[2]= 0 D[Subscript[f, 2], z]+ Subscript[f, 2]*(Subscript[f, 3]- Subscript[f, 1])+ 2*Subscript[\[Mu], 2]= 0 Failure Failure
Fail
2.828427124+2.828427124*I <- {f[1] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), f[3] = 2^(1/2)+I*2^(1/2), mu[2] = 2^(1/2)+I*2^(1/2)}
2.828427124-2.828427124*I <- {f[1] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), f[3] = 2^(1/2)+I*2^(1/2), mu[2] = 2^(1/2)-I*2^(1/2)}
-2.828427124-2.828427124*I <- {f[1] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), f[3] = 2^(1/2)+I*2^(1/2), mu[2] = -2^(1/2)-I*2^(1/2)}
-2.828427124+2.828427124*I <- {f[1] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), f[3] = 2^(1/2)+I*2^(1/2), mu[2] = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Skip
32.2#Ex5 ${\displaystyle{\displaystyle\frac{\mathrm{d}f_{3}}{\mathrm{d}z}+f_{3}(f_{1}-f_% {2})+2\mu_{3}=0}}$ diff(f[3], z)+ f[3]*(f[1]- f[2])+ 2*mu[3]= 0 D[Subscript[f, 3], z]+ Subscript[f, 3]*(Subscript[f, 1]- Subscript[f, 2])+ 2*Subscript[\[Mu], 3]= 0 Failure Failure
Fail
2.828427124+2.828427124*I <- {f[1] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), f[3] = 2^(1/2)+I*2^(1/2), mu[3] = 2^(1/2)+I*2^(1/2)}
2.828427124-2.828427124*I <- {f[1] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), f[3] = 2^(1/2)+I*2^(1/2), mu[3] = 2^(1/2)-I*2^(1/2)}
-2.828427124-2.828427124*I <- {f[1] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), f[3] = 2^(1/2)+I*2^(1/2), mu[3] = -2^(1/2)-I*2^(1/2)}
-2.828427124+2.828427124*I <- {f[1] = 2^(1/2)+I*2^(1/2), f[2] = 2^(1/2)+I*2^(1/2), f[3] = 2^(1/2)+I*2^(1/2), mu[3] = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Fail
Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[μ, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[2.8284271247461903, -2.8284271247461903] <- {Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[μ, 3], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[μ, 3], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-2.8284271247461903, 2.8284271247461903] <- {Rule[Subscript[f, 1], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 2], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[f, 3], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Subscript[μ, 3], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
32.2#Ex6 ${\displaystyle{\displaystyle z\frac{\mathrm{d}f_{1}}{\mathrm{d}z}=f_{1}f_{3}(f% _{2}-f_{4})+(\tfrac{1}{2}-\mu_{3})f_{1}+\mu_{1}f_{3}}}$ z*diff(f[1], z)= f[1]*f[3]*(f[2]- f[4])+((1)/(2)- mu[3])* f[1]+ mu[1]*f[3] z*D[Subscript[f, 1], z]= Subscript[f, 1]*Subscript[f, 3]*(Subscript[f, 2]- Subscript[f, 4])+(Divide[1,2]- Subscript[\[Mu], 3])* Subscript[f, 1]+ Subscript[\[Mu], 1]*Subscript[f, 3] Failure Failure Skip Skip
32.2#Ex7 ${\displaystyle{\displaystyle z\frac{\mathrm{d}f_{2}}{\mathrm{d}z}=f_{2}f_{4}(f% _{3}-f_{1})+(\tfrac{1}{2}-\mu_{4})f_{2}+\mu_{2}f_{4}}}$ z*diff(f[2], z)= f[2]*f[4]*(f[3]- f[1])+((1)/(2)- mu[4])* f[2]+ mu[2]*f[4] z*D[Subscript[f, 2], z]= Subscript[f, 2]*Subscript[f, 4]*(Subscript[f, 3]- Subscript[f, 1])+(Divide[1,2]- Subscript[\[Mu], 4])* Subscript[f, 2]+ Subscript[\[Mu], 2]*Subscript[f, 4] Failure Failure Skip Skip
32.2#Ex8 ${\displaystyle{\displaystyle z\frac{\mathrm{d}f_{3}}{\mathrm{d}z}=f_{3}f_{1}(f% _{4}-f_{2})+(\tfrac{1}{2}-\mu_{1})f_{3}+\mu_{3}f_{1}}}$ z*diff(f[3], z)= f[3]*f[1]*(f[4]- f[2])+((1)/(2)- mu[1])* f[3]+ mu[3]*f[1] z*D[Subscript[f, 3], z]= Subscript[f, 3]*Subscript[f, 1]*(Subscript[f, 4]- Subscript[f, 2])+(Divide[1,2]- Subscript[\[Mu], 1])* Subscript[f, 3]+ Subscript[\[Mu], 3]*Subscript[f, 1] Failure Failure Skip Skip
32.2#Ex9 ${\displaystyle{\displaystyle z\frac{\mathrm{d}f_{4}}{\mathrm{d}z}=f_{4}f_{2}(f% _{1}-f_{3})+(\tfrac{1}{2}-\mu_{2})f_{4}+\mu_{4}f_{2}}}$ z*diff(f[4], z)= f[4]*f[2]*(f[1]- f[3])+((1)/(2)- mu[2])* f[4]+ mu[4]*f[2] z*D[Subscript[f, 4], z]= Subscript[f, 4]*Subscript[f, 2]*(Subscript[f, 1]- Subscript[f, 3])+(Divide[1,2]- Subscript[\[Mu], 2])* Subscript[f, 4]+ Subscript[\[Mu], 4]*Subscript[f, 2] Failure Failure Skip Skip
32.2.E27 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}W}{{\mathrm{d}\zeta}^{2}}=6W% ^{2}+\zeta+\epsilon^{6}(2W^{3}+\zeta W)}}$ diff(W, [zeta$(2)])= 6*(W)^(2)+ zeta + (epsilon)^(6)*(2*(W)^(3)+ zeta*W) D[W, {\[zeta], 2}]= 6*(W)^(2)+ \[zeta]+ (\[Epsilon])^(6)*(2*(W)^(3)+ \[zeta]*W) Failure Failure Fail -981.4915554-749.4915558*I <- {W = 2^(1/2)+I*2^(1/2), epsilon = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)+I*2^(1/2)} -725.4915558-490.6631292*I <- {W = 2^(1/2)+I*2^(1/2), epsilon = 2^(1/2)+I*2^(1/2), zeta = 2^(1/2)-I*2^(1/2)} -466.6631292-746.6631286*I <- {W = 2^(1/2)+I*2^(1/2), epsilon = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)-I*2^(1/2)} -722.6631286-1005.491555*I <- {W = 2^(1/2)+I*2^(1/2), epsilon = 2^(1/2)+I*2^(1/2), zeta = -2^(1/2)+I*2^(1/2)} ... skip entries to safe data Error 32.3.E2 ${\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}u}{{\mathrm{d}x}^{2}}=3u^{5}% +2xu^{3}+\left(\tfrac{1}{4}x^{2}-\nu-\tfrac{1}{2}\right)u}}$ diff(u, [x$(2)])= 3*(u)^(5)+ 2*x*(u)^(3)+((1)/(4)*(x)^(2)- nu -(1)/(2))* u D[u, {x, 2}]= 3*(u)^(5)+ 2*x*(u)^(3)+(Divide[1,4]*(x)^(2)- \[Nu]-Divide[1,2])* u Failure Failure
Fail
79.54951279+60.92209581*I <- {nu = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), x = 1}
89.80256111+48.54772715*I <- {nu = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), x = 2}
99.34850267+35.46625170*I <- {nu = 2^(1/2)+I*2^(1/2), u = 2^(1/2)+I*2^(1/2), x = 3}
83.54951279-56.92209581*I <- {nu = 2^(1/2)+I*2^(1/2), u = 2^(1/2)-I*2^(1/2), x = 1}
... skip entries to safe data
Fail
Complex[79.5495128834866, 60.92209588551708] <- {Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[89.80256121069154, 48.5477272147525] <- {Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 2], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[99.34850275670993, 35.46625176280137] <- {Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 3], Rule[ν, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[83.5495128834866, 56.92209588551708] <- {Rule[u, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[x, 1], Rule[ν, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
32.4#Ex1 ${\displaystyle{\displaystyle\frac{\partial\boldsymbol{{\Psi}}}{\partial\lambda% }=\mathbf{A}(z,\lambda)\boldsymbol{{\Psi}}}}$ diff(Psi, lambda)= A*(z , lambda)* Psi D[\[CapitalPsi], \[Lambda]]= A*(z , \[Lambda])* \[CapitalPsi] Failure Failure Error Error
32.4#Ex2 ${\displaystyle{\displaystyle\frac{\partial\boldsymbol{{\Psi}}}{\partial z}=% \mathbf{B}(z,\lambda)\boldsymbol{{\Psi}}}}$ diff(Psi, z)= B*(z , lambda)* Psi D[\[CapitalPsi], z]= B*(z , \[Lambda])* \[CapitalPsi] Failure Failure Error Error
32.4.E3 ${\displaystyle{\displaystyle\frac{\partial\mathbf{A}}{\partial z}-\frac{% \partial\mathbf{B}}{\partial\lambda}+\mathbf{A}\mathbf{B}-\mathbf{B}\mathbf{A}% =0}}$ diff(A, z)- diff(B, lambda)+ A*B - B*A = 0 D[A, z]- D[B, \[Lambda]]+ A*B - B*A = 0 Successful Successful - -
32.6#Ex1 ${\displaystyle{\displaystyle\frac{\mathrm{d}q}{\mathrm{d}z}=\frac{\partial% \mathrm{H}}{\partial p}}}$ diff(q, z)= diff(H, p) D[q, z]= D[H, p] Successful Successful - -
32.6#Ex2 ${\displaystyle{\displaystyle\frac{\mathrm{d}p}{\mathrm{d}z}=-\frac{\partial% \mathrm{H}}{\partial q}}}$ diff(p, z)= - diff(H, q) D[p, z]= - D[H, q] Successful Successful - -
32.8.E8 ${\displaystyle{\displaystyle\sum_{m=0}^{\infty}p_{m}(z)\lambda^{m}=\exp\left(z% \lambda-\tfrac{4}{3}\lambda^{3}\right)}}$ sum(p[m]*(z)* (lambda)^(m), m = 0..infinity)= exp(z*lambda -(4)/(3)*(lambda)^(3)) Sum[Subscript[p, m]*(z)* (\[Lambda])^(m), {m, 0, Infinity}]= Exp[z*\[Lambda]-Divide[4,3]*(\[Lambda])^(3)] Failure Failure Skip Skip
32.10.E5 ${\displaystyle{\displaystyle\phi(z)=C_{1}\mathrm{Ai}\left(-2^{-1/3}z\right)+C_% {2}\mathrm{Bi}\left(-2^{-1/3}z\right)}}$ phi*(z)= C[1]*AiryAi(- (2)^(- 1/ 3)* z)+ C[2]*AiryBi(- (2)^(- 1/ 3)* z) \[Phi]*(z)= Subscript[C, 1]*AiryAi[- (2)^(- 1/ 3)* z]+ Subscript[C, 2]*AiryBi[- (2)^(- 1/ 3)* z] Failure Failure
Fail
-2.625238972+3.502678312*I <- {phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), C[1] = 2^(1/2)+I*2^(1/2), C[2] = 2^(1/2)+I*2^(1/2)}
-.2695111060+3.916247040*I <- {phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), C[1] = 2^(1/2)+I*2^(1/2), C[2] = 2^(1/2)-I*2^(1/2)}
.144057622+1.560519174*I <- {phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), C[1] = 2^(1/2)+I*2^(1/2), C[2] = -2^(1/2)-I*2^(1/2)}
-2.211670244+1.146950446*I <- {phi = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), C[1] = 2^(1/2)+I*2^(1/2), C[2] = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Skip
32.10.E14 ${\displaystyle{\displaystyle\phi(z)=z^{\nu}\left(C_{1}J_{\nu}\left(\zeta\right% )+C_{2}Y_{\nu}\left(\zeta\right)\right)}}$ phi*(z)= (z)^(nu)*(C[1]*BesselJ(nu, zeta)+ C[2]*BesselY(nu, zeta)) \[Phi]*(z)= (z)^(\[Nu])*(Subscript[C, 1]*BesselJ[\[Nu], \[zeta]]+ Subscript[C, 2]*BesselY[\[Nu], \[zeta]]) Failure Failure Skip Error
32.10.E19 ${\displaystyle{\displaystyle\phi(z)=\left(C_{1}U\left(a,\sqrt{2}z\right)+C_{2}% V\left(a,\sqrt{2}z\right)\right)\exp\left(\tfrac{1}{2}\varepsilon z^{2}\right)}}$ phi*(z)=(C[1]*CylinderU(a, sqrt(2)*z)+ C[2]*CylinderV(a, sqrt(2)*z))* exp((1)/(2)*varepsilon*(z)^(2)) Error Failure Error Skip -
32.10.E27 ${\displaystyle{\displaystyle\phi(z)=\frac{C_{1}M_{\kappa,\mu}\left(\zeta\right% )+C_{2}W_{\kappa,\mu}\left(\zeta\right)}{\zeta^{(a-b+1)/2}}\exp\left(\tfrac{1}% {2}\zeta\right)}}$ phi*(z)=(C[1]*WhittakerM(kappa, mu, zeta)+ C[2]*WhittakerW(kappa, mu, zeta))/((zeta)^((a - b + 1)/ 2))*exp((1)/(2)*zeta) \[Phi]*(z)=Divide[Subscript[C, 1]*WhittakerM[\[Kappa], \[Mu], \[zeta]]+ Subscript[C, 2]*WhittakerW[\[Kappa], \[Mu], \[zeta]],(\[zeta])^((a - b + 1)/ 2)]*Exp[Divide[1,2]*\[zeta]] Failure Failure Skip Error
32.10#Ex1 ${\displaystyle{\displaystyle w(z)=\frac{\zeta-1}{a\phi(\zeta)}\frac{\mathrm{d}% \phi}{\mathrm{d}\zeta}}}$ w*(z)=(zeta - 1)/(a*phi*(zeta))*diff(phi, zeta) w*(z)=Divide[\[zeta]- 1,a*\[Phi]*(\[zeta])]*D[\[Phi], \[zeta]] Failure Failure
Fail
0.+3.999999998*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2)}
3.999999998+0.*I <- {w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
0.-3.999999998*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)-I*2^(1/2)}
-3.999999998+0.*I <- {w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
32.10.E31 ${\displaystyle{\displaystyle\phi(\zeta)=C_{1}F\left(b,-a;b+c;\zeta\right)+C_{2% }\zeta^{-b+1-c}\*F\left(-a-b-c+1,-c+1;2-b-c;\zeta\right)}}$ phi*(zeta)= C[1]*hypergeom([b, - a], [b + c], zeta)+ C[2]*(zeta)^(- b + 1 - c)* hypergeom([- a - b - c + 1, - c + 1], [2 - b - c], zeta) \[Phi]*(\[zeta])= Subscript[C, 1]*Hypergeometric2F1[b, - a, b + c, \[zeta]]+ Subscript[C, 2]*(\[zeta])^(- b + 1 - c)* Hypergeometric2F1[- a - b - c + 1, - c + 1, 2 - b - c, \[zeta]] Failure Failure Skip Error
32.10.E32 ${\displaystyle{\displaystyle u=\int_{0}^{\Lambda}\frac{\mathrm{d}t}{\sqrt{t(t-% 1)(t-z)}}}}$ u = int((1)/(sqrt(t*(t - 1)*(t - z))), t = 0..Lambda) u = Integrate[Divide[1,Sqrt[t*(t - 1)*(t - z)]], {t, 0, \[CapitalLambda]}] Failure Failure Skip Error
32.10.E33 ${\displaystyle{\displaystyle z(1-z)\frac{{\mathrm{d}}^{2}\phi}{{\mathrm{d}z}^{% 2}}+(1-2z)\frac{\mathrm{d}\phi}{\mathrm{d}z}-\tfrac{1}{4}\phi=0}}$ z*(1 - z)* diff(phi, [z\$(2)])+(1 - 2*z)* diff(phi, z)-(1)/(4)*phi = 0 z*(1 - z)* D[\[Phi], {z, 2}]+(1 - 2*z)* D[\[Phi], z]-Divide[1,4]*\[Phi]= 0 Failure Failure
Fail
-.3535533905-.3535533905*I <- {phi = 2^(1/2)+I*2^(1/2)}
-.3535533905+.3535533905*I <- {phi = 2^(1/2)-I*2^(1/2)}
.3535533905+.3535533905*I <- {phi = -2^(1/2)-I*2^(1/2)}
.3535533905-.3535533905*I <- {phi = -2^(1/2)+I*2^(1/2)}
Error
32.11.E2 ${\displaystyle{\displaystyle\phi(x)=(24)^{1/4}\left(\tfrac{4}{5}|x|^{5/4}-% \tfrac{5}{8}d^{2}\ln|x|\right)}}$ phi*(x)=(24)^(1/ 4)*((4)/(5)*(abs(x))^(5/ 4)-(5)/(8)*(d)^(2)* ln(abs(x))) \[Phi]*(x)=(24)^(1/ 4)*(Divide[4,5]*(Abs[x])^(5/ 4)-Divide[5,8]*(d)^(2)* Log[Abs[x]]) Failure Failure
Fail
-.356477509+1.414213562*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 1}
-1.383009716+6.663894383*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 2}
-2.748440825+10.32171246*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 3}
-.356477509-1.414213562*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2), x = 1}
... skip entries to safe data
Error
32.11.E7 ${\displaystyle{\displaystyle\phi(x)=\tfrac{2}{3}|x|^{3/2}-\tfrac{3}{4}d^{2}\ln% |x|}}$ phi*(x)=(2)/(3)*(abs(x))^(3/ 2)-(3)/(4)*(d)^(2)* ln(abs(x)) \[Phi]*(x)=Divide[2,3]*(Abs[x])^(3/ 2)-Divide[3,4]*(d)^(2)* Log[Abs[x]] Failure Failure
Fail
.7475468953+1.414213562*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 1}
.9428090418+4.907868665*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 2}
.778539070+7.538477552*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 3}
.7475468953-1.414213562*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2), x = 1}
... skip entries to safe data
Error
32.11.E8 ${\displaystyle{\displaystyle d^{2}=-\pi^{-1}\ln\left(1-k^{2}\right)}}$ (d)^(2)= - (Pi)^(- 1)* ln(1 - (k)^(2)) (d)^(2)= - (Pi)^(- 1)* Log[1 - (k)^(2)] Failure Failure
Fail
Float(-infinity)+3.999999998*I <- {d = 2^(1/2)+I*2^(1/2), k = 1}
.3496991526+4.999999998*I <- {d = 2^(1/2)+I*2^(1/2), k = 2}
.6619068004+4.999999998*I <- {d = 2^(1/2)+I*2^(1/2), k = 3}
Float(-infinity)-3.999999998*I <- {d = 2^(1/2)-I*2^(1/2), k = 1}
... skip entries to safe data
Error
32.11.E9 ${\displaystyle{\displaystyle\theta_{0}=\tfrac{3}{2}d^{2}\ln 2+\operatorname{ph% }\Gamma\left(1-\tfrac{1}{2}id^{2}\right)+\tfrac{1}{4}\pi(1-2\operatorname{sign% }\left(k\right))}}$ theta[0]=(3)/(2)*(d)^(2)* ln(2)+ argument(GAMMA(1 -(1)/(2)*I*(d)^(2)))+(1)/(4)*Pi*(1 - 2*signum(k)) Subscript[\[Theta], 0]=Divide[3,2]*(d)^(2)* Log[2]+ Arg[Gamma[1 -Divide[1,2]*I*(d)^(2)]]+Divide[1,4]*Pi*(1 - 2*Sign[k]) Failure Failure
Fail
2.199611726-2.744669520*I <- {d = 2^(1/2)+I*2^(1/2), theta[0] = 2^(1/2)+I*2^(1/2), k = 1}
2.199611726-2.744669520*I <- {d = 2^(1/2)+I*2^(1/2), theta[0] = 2^(1/2)+I*2^(1/2), k = 2}
2.199611726-2.744669520*I <- {d = 2^(1/2)+I*2^(1/2), theta[0] = 2^(1/2)+I*2^(1/2), k = 3}
2.199611726-5.573096644*I <- {d = 2^(1/2)+I*2^(1/2), theta[0] = 2^(1/2)-I*2^(1/2), k = 1}
... skip entries to safe data
Error
32.11.E14 ${\displaystyle{\displaystyle\phi(x)=\tfrac{2}{3}|x|^{3/2}+\tfrac{3}{4}d^{2}\ln% |x|}}$ phi*(x)=(2)/(3)*(abs(x))^(3/ 2)+(3)/(4)*(d)^(2)* ln(abs(x)) \[Phi]*(x)=Divide[2,3]*(Abs[x])^(3/ 2)+Divide[3,4]*(d)^(2)* Log[Abs[x]] Failure Failure
Fail
.7475468953+1.414213562*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 1}
.9428090418+.748985583*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 2}
.778539070+.946803820*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 3}
.7475468953-1.414213562*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2), x = 1}
... skip entries to safe data
Error
32.11.E15 ${\displaystyle{\displaystyle\chi+\tfrac{3}{2}d^{2}\ln 2-\tfrac{1}{4}\pi-% \operatorname{ph}\Gamma\left(\tfrac{1}{2}id^{2}\right)=n\pi}}$ chi +(3)/(2)*(d)^(2)* ln(2)-(1)/(4)*Pi - argument(GAMMA((1)/(2)*I*(d)^(2)))= n*Pi \[Chi]+Divide[3,2]*(d)^(2)* Log[2]-Divide[1,4]*Pi - Arg[Gamma[Divide[1,2]*I*(d)^(2)]]= n*Pi Failure Failure
Fail
-4.083573582+5.573096644*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)+I*2^(1/2), n = 1}
-7.225166236+5.573096644*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)+I*2^(1/2), n = 2}
-10.36675889+5.573096644*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)+I*2^(1/2), n = 3}
-2.512777256-2.744669520*I <- {chi = 2^(1/2)+I*2^(1/2), d = 2^(1/2)-I*2^(1/2), n = 1}
... skip entries to safe data
Error
32.11.E17 ${\displaystyle{\displaystyle d^{2}=\pi^{-1}\ln\left(1+k^{2}\right)}}$ (d)^(2)= (Pi)^(- 1)* ln(1 + (k)^(2)) (d)^(2)= (Pi)^(- 1)* Log[1 + (k)^(2)] Failure Failure Skip Error
32.11.E18 ${\displaystyle{\displaystyle\chi+\tfrac{3}{2}d^{2}\ln 2-\tfrac{1}{4}\pi-% \operatorname{ph}\Gamma\left(\tfrac{1}{2}id^{2}\right)<>n\pi}}$ chi +(3)/(2)*(d)^(2)* ln(2)-(1)/(4)*Pi - argument(GAMMA((1)/(2)*I*(d)^(2)))< > n*Pi \[Chi]+Divide[3,2]*(d)^(2)* Log[2]-Divide[1,4]*Pi - Arg[Gamma[Divide[1,2]*I*(d)^(2)]]< > n*Pi Failure Failure Error Error
32.11.E20 ${\displaystyle{\displaystyle\psi(x)=\tfrac{2}{3}\sqrt{2}x^{3/2}-\tfrac{3}{2}% \rho^{2}\ln x}}$ psi*(x)=(2)/(3)*sqrt(2)*(x)^(3/ 2)-(3)/(2)*(rho)^(2)* ln(x) \[Psi]*(x)=Divide[2,3]*Sqrt[2]*(x)^(3/ 2)-Divide[3,2]*(\[Rho])^(2)* Log[x] Failure Failure
Fail
.4714045206+1.414213562*I <- {psi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), x = 1}
.1617604583+6.987310206*I <- {psi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), x = 2}
-.656338799+10.83431442*I <- {psi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)+I*2^(1/2), x = 3}
.4714045206+1.414213562*I <- {psi = 2^(1/2)+I*2^(1/2), rho = 2^(1/2)-I*2^(1/2), x = 1}
... skip entries to safe data
Error
32.11.E21 ${\displaystyle{\displaystyle\sigma=-\operatorname{sign}\left(\Im s\right)}}$ sigma = - signum(Im(s)) \[Sigma]= - Sign[Im[s]] Failure Failure
Fail
2.414213562+1.414213562*I <- {s = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2)}
2.414213562-1.414213562*I <- {s = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2)}
-.414213562-1.414213562*I <- {s = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2)}
-.414213562+1.414213562*I <- {s = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
32.11.E22 ${\displaystyle{\displaystyle\rho^{2}=\pi^{-1}\ln\left((1+|s|^{2})/|2\Im s|% \right)}}$ (rho)^(2)= (Pi)^(- 1)* ln((1 +(abs(s))^(2))/abs(2*Im(s))) (\[Rho])^(2)= (Pi)^(- 1)* Log[(1 +(Abs[s])^(2))/Abs[2*Im[s]]] Failure Failure
Fail
-.1813465983+3.999999998*I <- {rho = 2^(1/2)+I*2^(1/2), s = 2^(1/2)+I*2^(1/2)}
-.1813465983+3.999999998*I <- {rho = 2^(1/2)+I*2^(1/2), s = 2^(1/2)-I*2^(1/2)}
-.1813465983+3.999999998*I <- {rho = 2^(1/2)+I*2^(1/2), s = -2^(1/2)-I*2^(1/2)}
-.1813465983+3.999999998*I <- {rho = 2^(1/2)+I*2^(1/2), s = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
32.11.E23 ${\displaystyle{\displaystyle\theta=-\tfrac{3}{4}\pi-\tfrac{7}{2}\rho^{2}\ln{2}% +\operatorname{ph}\left(1+s^{2}\right)+\operatorname{ph}\Gamma\left(i\rho^{2}% \right)}}$ theta = -(3)/(4)*Pi -(7)/(2)*(rho)^(2)* ln(2)+ argument(1 + (s)^(2))+ argument(GAMMA(I*(rho)^(2))) \[Theta]= -Divide[3,4]*Pi -Divide[7,2]*(\[Rho])^(2)* Log[2]+ Arg[1 + (s)^(2)]+ Arg[Gamma[I*(\[Rho])^(2)]] Failure Failure
Fail
.873794061+11.11827408*I <- {rho = 2^(1/2)+I*2^(1/2), s = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)+I*2^(1/2)}
.873794061+8.289846961*I <- {rho = 2^(1/2)+I*2^(1/2), s = 2^(1/2)+I*2^(1/2), theta = 2^(1/2)-I*2^(1/2)}
-1.954633063+8.289846961*I <- {rho = 2^(1/2)+I*2^(1/2), s = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)-I*2^(1/2)}
-1.954633063+11.11827408*I <- {rho = 2^(1/2)+I*2^(1/2), s = 2^(1/2)+I*2^(1/2), theta = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
32.11.E27 ${\displaystyle{\displaystyle\sigma=(2/\pi)\operatorname{arcsin}\left(\pi% \lambda\right)}}$ sigma =(2/ Pi)* arcsin(Pi*lambda) \[Sigma]=(2/ Pi)* ArcSin[Pi*\[Lambda]] Failure Failure
Fail
.9182444652-.197124803*I <- {lambda = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2)}
.9182444652-3.025551927*I <- {lambda = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2)}
-1.910182659-3.025551927*I <- {lambda = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2)}
-1.910182659-.197124803*I <- {lambda = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
32.11.E28 ${\displaystyle{\displaystyle B=2^{-2\sigma}\frac{{\Gamma^{2}}\left(\tfrac{1}{2% }(1-\sigma)\right)\Gamma\left(\tfrac{1}{2}(1+\sigma)+\nu\right)}{{\Gamma^{2}}% \left(\tfrac{1}{2}(1+\sigma)\right)\Gamma\left(\tfrac{1}{2}(1-\sigma)+\nu% \right)}}}$ B = (2)^(- 2*sigma)*((GAMMA((1)/(2)*(1 - sigma)))^(2)* GAMMA((1)/(2)*(1 + sigma)+ nu))/((GAMMA((1)/(2)*(1 + sigma)))^(2)* GAMMA((1)/(2)*(1 - sigma)+ nu)) B = (2)^(- 2*\[Sigma])*Divide[(Gamma[Divide[1,2]*(1 - \[Sigma])])^(2)* Gamma[Divide[1,2]*(1 + \[Sigma])+ \[Nu]],(Gamma[Divide[1,2]*(1 + \[Sigma])])^(2)* Gamma[Divide[1,2]*(1 - \[Sigma])+ \[Nu]]] Failure Failure
Fail
1.341555906+1.650216622*I <- {B = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)+I*2^(1/2)}
3.846316726+1.915270556*I <- {B = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), sigma = 2^(1/2)-I*2^(1/2)}
.222646953-2.456175086*I <- {B = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)-I*2^(1/2)}
1.808639547+1.332954715*I <- {B = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), sigma = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
32.11.E31 ${\displaystyle{\displaystyle h^{*}=\ifrac{1}{\left(\pi^{1/2}\Gamma\left(\nu+1% \right)\right)}}}$ (h)^(*)=(1)/((Pi)^(1/ 2)* GAMMA(nu + 1)) (h)^(*)=Divide[1,(Pi)^(1/ 2)* Gamma[\[Nu]+ 1]] Error Failure - Error
32.11.E34 ${\displaystyle{\displaystyle\phi(x)=\tfrac{1}{3}\sqrt{3}x^{2}-\tfrac{4}{3}d^{2% }\sqrt{3}\ln\left(\sqrt{2}|x|\right)}}$ phi*(x)=(1)/(3)*sqrt(3)*(x)^(2)-(4)/(3)*(d)^(2)*sqrt(3)*ln(sqrt(2)*abs(x)) \[Phi]*(x)=Divide[1,3]*Sqrt[3]*(x)^(2)-Divide[4,3]*(d)^(2)*Sqrt[3]*Log[Sqrt[2]*Abs[x]] Failure Failure
Fail
.8368632927+4.615723248*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 1}
.519026047+12.43295619*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 2}
-.953511738+17.59269598*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)+I*2^(1/2), x = 3}
.8368632927+1.787296124*I <- {d = 2^(1/2)+I*2^(1/2), phi = 2^(1/2)-I*2^(1/2), x = 1}
... skip entries to safe data
Error
32.11.E35 ${\displaystyle{\displaystyle d^{2}=-\tfrac{1}{4}\sqrt{3}\pi^{-1}\ln\left(1-|% \mu|^{2}\right)}}$ (d)^(2)= -(1)/(4)*sqrt(3)*(Pi)^(- 1)* ln(1 -(abs(mu))^(2)) (d)^(2)= -Divide[1,4]*Sqrt[3]*(Pi)^(- 1)* Log[1 -(Abs[\[Mu]])^(2)] Failure Failure
Fail
.1514241750+4.433012700*I <- {d = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2)}
.1514241750+4.433012700*I <- {d = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)-I*2^(1/2)}
.1514241750+4.433012700*I <- {d = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)-I*2^(1/2)}
.1514241750+4.433012700*I <- {d = 2^(1/2)+I*2^(1/2), mu = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
32.11.E36 ${\displaystyle{\displaystyle\theta_{0}=\tfrac{1}{3}d^{2}\sqrt{3}\ln 3+\tfrac{2% }{3}\pi\nu+\tfrac{7}{12}\pi+\operatorname{ph}\mu+\operatorname{ph}\Gamma\left(% -\tfrac{2}{3}i\sqrt{3}d^{2}\right)}}$ theta[0]=(1)/(3)*(d)^(2)*sqrt(3)*ln(3)+(2)/(3)*Pi*nu +(7)/(12)*Pi + argument(mu)+ argument(GAMMA(-(2)/(3)*I*sqrt(3)*(d)^(2))) Subscript[\[Theta], 0]=Divide[1,3]*(d)^(2)*Sqrt[3]*Log[3]+Divide[2,3]*Pi*\[Nu]+Divide[7,12]*Pi + Arg[\[Mu]]+ Arg[Gamma[-Divide[2,3]*I*Sqrt[3]*(d)^(2)]] Failure Failure
Fail
-4.165702275-4.084844799*I <- {d = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), theta[0] = 2^(1/2)+I*2^(1/2)}
-4.165702275-6.913271923*I <- {d = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), theta[0] = 2^(1/2)-I*2^(1/2)}
-6.994129399-6.913271923*I <- {d = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), theta[0] = -2^(1/2)-I*2^(1/2)}
-6.994129399-4.084844799*I <- {d = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), theta[0] = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
32.11.E37 ${\displaystyle{\displaystyle\mu=1+\left(\ifrac{2ih\pi^{3/2}\exp\left(-i\pi\nu% \right)}{\Gamma\left(-\nu\right)}\right)}}$ mu = 1 +((2*I*h*(Pi)^(3/ 2)* exp(- I*Pi*nu))/(GAMMA(- nu))) \[Mu]= 1 +(Divide[2*I*h*(Pi)^(3/ 2)* Exp[- I*Pi*\[Nu]],Gamma[- \[Nu]]]) Failure Failure
Fail
-14237.77906+14002.23390*I <- {h = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2)}
3.087580692+.7179287085*I <- {h = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)-I*2^(1/2)}
-.2354286281+1.240678506*I <- {h = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), nu = -2^(1/2)-I*2^(1/2)}
-3486.428322-3384.777319*I <- {h = 2^(1/2)+I*2^(1/2), mu = 2^(1/2)+I*2^(1/2), nu = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
32.13.E6 ${\displaystyle{\displaystyle u_{xt}=\sin u}}$ u[x*t]= sin(u) Subscript[u, x*t]= Sin[u] Failure Failure
Fail
-.737321978+1.112452092*I <- {u = 2^(1/2)+I*2^(1/2), u[x*t] = 2^(1/2)+I*2^(1/2)}
-.737321978-1.715975032*I <- {u = 2^(1/2)+I*2^(1/2), u[x*t] = 2^(1/2)-I*2^(1/2)}
-3.565749102-1.715975032*I <- {u = 2^(1/2)+I*2^(1/2), u[x*t] = -2^(1/2)-I*2^(1/2)}
-3.565749102+1.112452092*I <- {u = 2^(1/2)+I*2^(1/2), u[x*t] = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Error
32.14.E2 ${\displaystyle{\displaystyle F(s)=\exp\left(-\int_{s}^{\infty}(x-s)w^{2}(x)% \mathrm{d}x\right)}}$ F*(s)= exp(- int((x - s)* (w)^(2)*(x), x = s..infinity)) F*(s)= Exp[- Integrate[(x - s)* (w)^(2)*(x), {x, s, Infinity}]] Failure Failure Skip Error
32.15.E1 ${\displaystyle{\displaystyle\int_{-\infty}^{\infty}\exp\left(-\tfrac{1}{4}\xi^% {4}-z\xi^{2}\right)p_{m}(\xi)p_{n}(\xi)\mathrm{d}\xi=\delta_{m,n}}}$ int(exp(-(1)/(4)*(xi)^(4)- z*(xi)^(2))*p[m]*(xi)* p[n]*(xi), xi = - infinity..infinity)= KroneckerDelta[m, n] Integrate[Exp[-Divide[1,4]*(\[Xi])^(4)- z*(\[Xi])^(2)]*Subscript[p, m]*(\[Xi])* Subscript[p, n]*(\[Xi]), {\[Xi], - Infinity, Infinity}]= KroneckerDelta[m, n] Failure Failure Skip Error