Results of Bessel Functions

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DLMF Formula Maple Mathematica Symbolic
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10.2.E1 (z)^(2)* diff(w, [z$(2)])+ z*diff(w, z)+((z)^(2)- (nu)^(2))* w = 0 (z)^(2)* D[w, {z, 2}]+ z*D[w, z]+((z)^(2)- (\[Nu])^(2))* w = 0 Failure Failure
Fail
11.31370849-11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
11.31370849-11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)+I*2^(1/2), z = -2^(1/2)+I*2^(1/2)}
-11.31370849-11.31370849*I <- {nu = 2^(1/2)+I*2^(1/2), w = 2^(1/2)-I*2^(1/2), z = 2^(1/2)-I*2^(1/2)}
-11.31370849-11.31370849*I <- {nu = 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[-11.313708498984761, 11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-11.313708498984761, 11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.313708498984761, -11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[11.313708498984761, -11.313708498984761] <- {Rule[w, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[z, Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
10.2.E2 BesselJ(nu, z)=((1)/(2)*z)^(nu)* sum((- 1)^(k)*(((1)/(4)*(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)), k = 0..infinity) BesselJ[\[Nu], z]=(Divide[1,2]*z)^(\[Nu])* Sum[(- 1)^(k)*Divide[(Divide[1,4]*(z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]], {k, 0, Infinity}] Successful Successful - -
10.2.E3 BesselY(nu, z)=(BesselJ(nu, z)*cos(nu*Pi)- BesselJ(- nu, z))/(sin(nu*Pi)) BesselY[\[Nu], z]=Divide[BesselJ[\[Nu], z]*Cos[\[Nu]*Pi]- BesselJ[- \[Nu], z],Sin[\[Nu]*Pi]] Successful Successful - -
10.4#Ex1 BesselJ(- n, z)=(- 1)^(n)* BesselJ(n, z) BesselJ[- n, z]=(- 1)^(n)* BesselJ[n, z] Failure Failure Successful Successful
10.4#Ex2 BesselY(- n, z)=(- 1)^(n)* BesselY(n, z) BesselY[- n, z]=(- 1)^(n)* BesselY[n, z] Failure Failure Successful Successful
10.4#Ex3 HankelH1(- n, z)=(- 1)^(n)* HankelH1(n, z) HankelH1[- n, z]=(- 1)^(n)* HankelH1[n, z] Successful Failure - Successful
10.4#Ex4 HankelH2(- n, z)=(- 1)^(n)* HankelH2(n, z) HankelH2[- n, z]=(- 1)^(n)* HankelH2[n, z] Failure Failure Successful Successful
10.4#Ex5 HankelH1(nu, z)= BesselJ(nu, z)+ I*BesselY(nu, z) HankelH1[\[Nu], z]= BesselJ[\[Nu], z]+ I*BesselY[\[Nu], z] Failure Successful Successful -
10.4#Ex6 HankelH2(nu, z)= BesselJ(nu, z)- I*BesselY(nu, z) HankelH2[\[Nu], z]= BesselJ[\[Nu], z]- I*BesselY[\[Nu], z] Failure Successful Successful -
10.4#Ex7 BesselJ(nu, z)=(1)/(2)*(HankelH1(nu, z)+ HankelH2(nu, z)) BesselJ[\[Nu], z]=Divide[1,2]*(HankelH1[\[Nu], z]+ HankelH2[\[Nu], z]) Successful Successful - -
10.4#Ex8 BesselY(nu, z)=(1)/(2*I)*(HankelH1(nu, z)- HankelH2(nu, z)) BesselY[\[Nu], z]=Divide[1,2*I]*(HankelH1[\[Nu], z]- HankelH2[\[Nu], z]) Successful Successful - -
10.4.E5 BesselJ(nu, z)= csc(nu*Pi)*(BesselY(- nu, z)- BesselY(nu, z)*cos(nu*Pi)) BesselJ[\[Nu], z]= Csc[\[Nu]*Pi]*(BesselY[- \[Nu], z]- BesselY[\[Nu], z]*Cos[\[Nu]*Pi]) Successful Successful - -
10.4#Ex9 HankelH1(- nu, z)= exp(nu*Pi*I)*HankelH1(nu, z) HankelH1[- \[Nu], z]= Exp[\[Nu]*Pi*I]*HankelH1[\[Nu], z] Successful Failure - Successful
10.4#Ex10 HankelH2(- nu, z)= exp(- nu*Pi*I)*HankelH2(nu, z) HankelH2[- \[Nu], z]= Exp[- \[Nu]*Pi*I]*HankelH2[\[Nu], z] Successful Failure - Successful
10.4.E7 HankelH1(nu, z)= I*csc(nu*Pi)*(exp(- nu*Pi*I)*BesselJ(nu, z)- BesselJ(- nu, z)) HankelH1[\[Nu], z]= I*Csc[\[Nu]*Pi]*(Exp[- \[Nu]*Pi*I]*BesselJ[\[Nu], z]- BesselJ[- \[Nu], z]) Successful Successful - -
10.4.E7 I*csc(nu*Pi)*(exp(- nu*Pi*I)*BesselJ(nu, z)- BesselJ(- nu, z))= csc(nu*Pi)*(BesselY(- nu, z)- exp(- nu*Pi*I)*BesselY(nu, z)) I*Csc[\[Nu]*Pi]*(Exp[- \[Nu]*Pi*I]*BesselJ[\[Nu], z]- BesselJ[- \[Nu], z])= Csc[\[Nu]*Pi]*(BesselY[- \[Nu], z]- Exp[- \[Nu]*Pi*I]*BesselY[\[Nu], z]) Failure Successful Successful -
10.4.E8 HankelH2(nu, z)= I*csc(nu*Pi)*(BesselJ(- nu, z)- exp(nu*Pi*I)*BesselJ(nu, z)) HankelH2[\[Nu], z]= I*Csc[\[Nu]*Pi]*(BesselJ[- \[Nu], z]- Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], z]) Successful Successful - -
10.4.E8 I*csc(nu*Pi)*(BesselJ(- nu, z)- exp(nu*Pi*I)*BesselJ(nu, z))= csc(nu*Pi)*(BesselY(- nu, z)- exp(nu*Pi*I)*BesselY(nu, z)) I*Csc[\[Nu]*Pi]*(BesselJ[- \[Nu], z]- Exp[\[Nu]*Pi*I]*BesselJ[\[Nu], z])= Csc[\[Nu]*Pi]*(BesselY[- \[Nu], z]- Exp[\[Nu]*Pi*I]*BesselY[\[Nu], z]) Failure Successful Successful -
10.5.E1 (BesselJ(nu, z))*diff(BesselJ(- nu, z), z)-diff(BesselJ(nu, z), z)*(BesselJ(- nu, z))= BesselJ(nu + 1, z)*BesselJ(- nu, z)+ BesselJ(nu, z)*BesselJ(- nu - 1, z) Wronskian[{BesselJ[\[Nu], z], BesselJ[- \[Nu], z]}, z]= BesselJ[\[Nu]+ 1, z]*BesselJ[- \[Nu], z]+ BesselJ[\[Nu], z]*BesselJ[- \[Nu]- 1, z] Successful Successful - -
10.5.E1 BesselJ(nu + 1, z)*BesselJ(- nu, z)+ BesselJ(nu, z)*BesselJ(- nu - 1, z)= - 2*sin(nu*Pi)/(Pi*z) BesselJ[\[Nu]+ 1, z]*BesselJ[- \[Nu], z]+ BesselJ[\[Nu], z]*BesselJ[- \[Nu]- 1, z]= - 2*Sin[\[Nu]*Pi]/(Pi*z) Failure Successful Successful -
10.5.E2 (BesselJ(nu, z))*diff(BesselY(nu, z), z)-diff(BesselJ(nu, z), z)*(BesselY(nu, z))= BesselJ(nu + 1, z)*BesselY(nu, z)- BesselJ(nu, z)*BesselY(nu + 1, z) Wronskian[{BesselJ[\[Nu], z], BesselY[\[Nu], z]}, z]= BesselJ[\[Nu]+ 1, z]*BesselY[\[Nu], z]- BesselJ[\[Nu], z]*BesselY[\[Nu]+ 1, z] Successful Successful - -
10.5.E2 BesselJ(nu + 1, z)*BesselY(nu, z)- BesselJ(nu, z)*BesselY(nu + 1, z)= 2/(Pi*z) BesselJ[\[Nu]+ 1, z]*BesselY[\[Nu], z]- BesselJ[\[Nu], z]*BesselY[\[Nu]+ 1, z]= 2/(Pi*z) Failure Successful Successful -
10.5.E3 BesselJ(nu + 1, z)*HankelH1(nu, z)- BesselJ(nu, z)*HankelH1(nu + 1, z)= 2*I/(Pi*z) BesselJ[\[Nu]+ 1, z]*HankelH1[\[Nu], z]- BesselJ[\[Nu], z]*HankelH1[\[Nu]+ 1, z]= 2*I/(Pi*z) Failure Successful Successful -
10.5.E4 BesselJ(nu + 1, z)*HankelH2(nu, z)- BesselJ(nu, z)*HankelH2(nu + 1, z)= - 2*I/(Pi*z) BesselJ[\[Nu]+ 1, z]*HankelH2[\[Nu], z]- BesselJ[\[Nu], z]*HankelH2[\[Nu]+ 1, z]= - 2*I/(Pi*z) Failure Successful Successful -
10.5.E5 (HankelH1(nu, z))*diff(HankelH2(nu, z), z)-diff(HankelH1(nu, z), z)*(HankelH2(nu, z))= HankelH1(nu + 1, z)*HankelH2(nu, z)- HankelH1(nu, z)*HankelH2(nu + 1, z) Wronskian[{HankelH1[\[Nu], z], HankelH2[\[Nu], z]}, z]= HankelH1[\[Nu]+ 1, z]*HankelH2[\[Nu], z]- HankelH1[\[Nu], z]*HankelH2[\[Nu]+ 1, z] Successful Successful - -
10.5.E5 HankelH1(nu + 1, z)*HankelH2(nu, z)- HankelH1(nu, z)*HankelH2(nu + 1, z)= - 4*I/(Pi*z) HankelH1[\[Nu]+ 1, z]*HankelH2[\[Nu], z]- HankelH1[\[Nu], z]*HankelH2[\[Nu]+ 1, z]= - 4*I/(Pi*z) Failure Successful Successful -
10.6#Ex11 p[nu]= BesselJ(nu, a)*BesselY(nu, b)- BesselJ(nu, b)*BesselY(nu, a) Subscript[p, \[Nu]]= BesselJ[\[Nu], a]*BesselY[\[Nu], b]- BesselJ[\[Nu], b]*BesselY[\[Nu], a] Failure Failure
Fail
1.414213562+1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), p[nu] = 2^(1/2)+I*2^(1/2)}
1.414213562-1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), p[nu] = 2^(1/2)-I*2^(1/2)}
-1.414213562-1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), p[nu] = -2^(1/2)-I*2^(1/2)}
-1.414213562+1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), p[nu] = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Skip
10.6#Ex12 q[nu]= BesselJ(nu, a)*subs( temp=b, diff( BesselY(nu, temp), temp$(1) ) )- subs( temp=b, diff( BesselJ(nu, temp), temp$(1) ) )*BesselY(nu, a) Subscript[q, \[Nu]]= BesselJ[\[Nu], a]*(D[BesselY[\[Nu], temp], {temp, 1}]/.temp-> b)- (D[BesselJ[\[Nu], temp], {temp, 1}]/.temp-> b)*BesselY[\[Nu], a] Failure Failure
Fail
1.189134483+1.639292641*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), q[nu] = 2^(1/2)+I*2^(1/2)}
1.189134483-1.189134483*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), q[nu] = 2^(1/2)-I*2^(1/2)}
-1.639292641-1.189134483*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), q[nu] = -2^(1/2)-I*2^(1/2)}
-1.639292641+1.639292641*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), q[nu] = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Skip
10.6#Ex13 r[nu]= subs( temp=a, diff( BesselJ(nu, temp), temp$(1) ) )*BesselY(nu, b)- BesselJ(nu, b)*subs( temp=a, diff( BesselY(nu, temp), temp$(1) ) ) Subscript[r, \[Nu]]= (D[BesselJ[\[Nu], temp], {temp, 1}]/.temp-> a)*BesselY[\[Nu], b]- BesselJ[\[Nu], b]*(D[BesselY[\[Nu], temp], {temp, 1}]/.temp-> a) Failure Failure
Fail
1.639292641+1.189134483*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), r[nu] = 2^(1/2)+I*2^(1/2)}
1.639292641-1.639292641*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), r[nu] = 2^(1/2)-I*2^(1/2)}
-1.189134483-1.639292641*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), r[nu] = -2^(1/2)-I*2^(1/2)}
-1.189134483+1.189134483*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), r[nu] = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Skip
10.6#Ex14 s[nu]= subs( temp=a, diff( BesselJ(nu, temp), temp$(1) ) )*subs( temp=b, diff( BesselY(nu, temp), temp$(1) ) )- subs( temp=b, diff( BesselJ(nu, temp), temp$(1) ) )*subs( temp=a, diff( BesselY(nu, temp), temp$(1) ) ) Subscript[s, \[Nu]]= (D[BesselJ[\[Nu], temp], {temp, 1}]/.temp-> a)*(D[BesselY[\[Nu], temp], {temp, 1}]/.temp-> b)- (D[BesselJ[\[Nu], temp], {temp, 1}]/.temp-> b)*(D[BesselY[\[Nu], temp], {temp, 1}]/.temp-> a) Failure Failure
Fail
1.414213562+1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), s[nu] = 2^(1/2)+I*2^(1/2)}
1.414213562-1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), s[nu] = 2^(1/2)-I*2^(1/2)}
-1.414213562-1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), s[nu] = -2^(1/2)-I*2^(1/2)}
-1.414213562+1.414213562*I <- {a = 2^(1/2)+I*2^(1/2), b = 2^(1/2)+I*2^(1/2), nu = 2^(1/2)+I*2^(1/2), s[nu] = -2^(1/2)+I*2^(1/2)}
... skip entries to safe data
Skip
10.8.E1 BesselY(n, z)= -(((1)/(2)*z)^(- n))/(Pi)*sum((factorial(n - k - 1))/(factorial(k))*((1)/(4)*(z)^(2))^(k), k = 0..n - 1)+(2)/(Pi)*ln((1)/(2)*z)*BesselJ(n, z)-(((1)/(2)*z)^(n))/(Pi)*sum((Psi(k + 1)+ Psi(n + k + 1))*((-(1)/(4)*(z)^(2))^(k))/(factorial(k)*factorial(n + k)), k = 0..infinity) BesselY[n, z]= -Divide[(Divide[1,2]*z)^(- n),Pi]*Sum[Divide[(n - k - 1)!,(k)!]*(Divide[1,4]*(z)^(2))^(k), {k, 0, n - 1}]+Divide[2,Pi]*Log[Divide[1,2]*z]*BesselJ[n, z]-Divide[(Divide[1,2]*z)^(n),Pi]*Sum[(PolyGamma[k + 1]+ PolyGamma[n + k + 1])*Divide[(-Divide[1,4]*(z)^(2))^(k),(k)!*(n + k)!], {k, 0, Infinity}] Error Failure - Successful
10.9.E1 BesselJ(0, z)=(1)/(Pi)*int(cos(z*sin(theta)), theta = 0..Pi) BesselJ[0, z]=Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]], {\[Theta], 0, Pi}] Successful Failure - Successful
10.9.E1 (1)/(Pi)*int(cos(z*sin(theta)), theta = 0..Pi)=(1)/(Pi)*int(cos(z*cos(theta)), theta = 0..Pi) Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]], {\[Theta], 0, Pi}]=Divide[1,Pi]*Integrate[Cos[z*Cos[\[Theta]]], {\[Theta], 0, Pi}] Successful Failure - Successful
10.9.E2 BesselJ(n, z)=(1)/(Pi)*int(cos(z*sin(theta)- n*theta), theta = 0..Pi) BesselJ[n, z]=Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- n*\[Theta]], {\[Theta], 0, Pi}] Failure Failure Skip Successful
10.9.E2 (1)/(Pi)*int(cos(z*sin(theta)- n*theta), theta = 0..Pi)=((I)^(- n))/(Pi)*int(exp(I*z*cos(theta))*cos(n*theta), theta = 0..Pi) Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- n*\[Theta]], {\[Theta], 0, Pi}]=Divide[(I)^(- n),Pi]*Integrate[Exp[I*z*Cos[\[Theta]]]*Cos[n*\[Theta]], {\[Theta], 0, Pi}] Failure Failure Skip Successful
10.9.E3 BesselY(0, z)=(4)/((Pi)^(2))*int(cos(z*cos(theta))*(gamma + ln(2*z*(sin(theta))^(2))), theta = 0..(1)/(2)*Pi) BesselY[0, z]=Divide[4,(Pi)^(2)]*Integrate[Cos[z*Cos[\[Theta]]]*(EulerGamma + Log[2*z*(Sin[\[Theta]])^(2)]), {\[Theta], 0, Divide[1,2]*Pi}] Failure Failure Skip Successful
10.9.E4 BesselJ(nu, z)=(((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(cos(z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi) BesselJ[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Cos[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}] Failure Failure Skip Successful
10.9.E4 (((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int(cos(z*cos(theta))*(sin(theta))^(2*nu), theta = 0..Pi)=(2*((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*int((1 - (t)^(2))^(nu -(1)/(2))* cos(z*t), t = 0..1) Divide[(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[Cos[z*Cos[\[Theta]]]*(Sin[\[Theta]])^(2*\[Nu]), {\[Theta], 0, Pi}]=Divide[2*(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Cos[z*t], {t, 0, 1}] Failure Failure Skip Skip
10.9.E5 BesselY(nu, z)=(2*((1)/(2)*z)^(nu))/((Pi)^((1)/(2))* GAMMA(nu +(1)/(2)))*(int((1 - (t)^(2))^(nu -(1)/(2))* sin(z*t), t = 0..1)- int(exp(- z*t)*(1 + (t)^(2))^(nu -(1)/(2)), t = 0..infinity)) BesselY[\[Nu], z]=Divide[2*(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[1,2])* Gamma[\[Nu]+Divide[1,2]]]*(Integrate[(1 - (t)^(2))^(\[Nu]-Divide[1,2])* Sin[z*t], {t, 0, 1}]- Integrate[Exp[- z*t]*(1 + (t)^(2))^(\[Nu]-Divide[1,2]), {t, 0, Infinity}]) Successful Failure - Skip
10.9.E6 BesselJ(nu, z)=(1)/(Pi)*int(cos(z*sin(theta)- nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- z*sinh(t)- nu*t), t = 0..infinity) BesselJ[\[Nu], z]=Divide[1,Pi]*Integrate[Cos[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- z*Sinh[t]- \[Nu]*t], {t, 0, Infinity}] Failure Failure Skip Error
10.9.E7 BesselY(nu, z)=(1)/(Pi)*int(sin(z*sin(theta)- nu*theta), theta = 0..Pi)-(1)/(Pi)*int((exp(nu*t)+ exp(- nu*t)*cos(nu*Pi))* exp(- z*sinh(t)), t = 0..infinity) BesselY[\[Nu], z]=Divide[1,Pi]*Integrate[Sin[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}]-Divide[1,Pi]*Integrate[(Exp[\[Nu]*t]+ Exp[- \[Nu]*t]*Cos[\[Nu]*Pi])* Exp[- z*Sinh[t]], {t, 0, Infinity}] Failure Failure Skip Error
10.9#Ex1 BesselJ(nu, x)=(2)/(Pi)*int(sin(x*cosh(t)-(1)/(2)*nu*Pi)*cosh(nu*t), t = 0..infinity) BesselJ[\[Nu], x]=Divide[2,Pi]*Integrate[Sin[x*Cosh[t]-Divide[1,2]*\[Nu]*Pi]*Cosh[\[Nu]*t], {t, 0, Infinity}] Failure Failure Skip Error
10.9#Ex2 BesselY(nu, x)= -(2)/(Pi)*int(cos(x*cosh(t)-(1)/(2)*nu*Pi)*cosh(nu*t), t = 0..infinity) BesselY[\[Nu], x]= -Divide[2,Pi]*Integrate[Cos[x*Cosh[t]-Divide[1,2]*\[Nu]*Pi]*Cosh[\[Nu]*t], {t, 0, Infinity}] Failure Failure Skip Error
10.9#Ex3 BesselJ(0, x)=(2)/(Pi)*int(sin(x*cosh(t)), t = 0..infinity) BesselJ[0, x]=Divide[2,Pi]*Integrate[Sin[x*Cosh[t]], {t, 0, Infinity}] Failure Failure Skip Error
10.9#Ex4 BesselY(0, x)= -(2)/(Pi)*int(cos(x*cosh(t)), t = 0..infinity) BesselY[0, x]= -Divide[2,Pi]*Integrate[Cos[x*Cosh[t]], {t, 0, Infinity}] Failure Failure Skip Error
10.9.E10 HankelH1(nu, z)=(exp(-(1)/(2)*nu*Pi*I))/(Pi*I)*int(exp(I*z*cosh(t)- nu*t), t = - infinity..infinity) HankelH1[\[Nu], z]=Divide[Exp[-Divide[1,2]*\[Nu]*Pi*I],Pi*I]*Integrate[Exp[I*z*Cosh[t]- \[Nu]*t], {t, - Infinity, Infinity}] Failure Failure Skip Error
10.9.E11 HankelH2(nu, z)= -(exp((1)/(2)*nu*Pi*I))/(Pi*I)*int(exp(- I*z*cosh(t)- nu*t), t = - infinity..infinity) HankelH2[\[Nu], z]= -Divide[Exp[Divide[1,2]*\[Nu]*Pi*I],Pi*I]*Integrate[Exp[- I*z*Cosh[t]- \[Nu]*t], {t, - Infinity, Infinity}] Failure Failure Skip Error
10.9#Ex5 BesselJ(nu, x)=(2*((1)/(2)*x)^(- nu))/((Pi)^((1)/(2))* GAMMA((1)/(2)- nu))*int((sin(x*t))/(((t)^(2)- 1)^(nu +(1)/(2))), t = 1..infinity) BesselJ[\[Nu], x]=Divide[2*(Divide[1,2]*x)^(- \[Nu]),(Pi)^(Divide[1,2])* Gamma[Divide[1,2]- \[Nu]]]*Integrate[Divide[Sin[x*t],((t)^(2)- 1)^(\[Nu]+Divide[1,2])], {t, 1, Infinity}] Successful Failure - Successful
10.9#Ex6 BesselY(nu, x)= -(2*((1)/(2)*x)^(- nu))/((Pi)^((1)/(2))* GAMMA((1)/(2)- nu))*int((cos(x*t))/(((t)^(2)- 1)^(nu +(1)/(2))), t = 1..infinity) BesselY[\[Nu], x]= -Divide[2*(Divide[1,2]*x)^(- \[Nu]),(Pi)^(Divide[1,2])* Gamma[Divide[1,2]- \[Nu]]]*Integrate[Divide[Cos[x*t],((t)^(2)- 1)^(\[Nu]+Divide[1,2])], {t, 1, Infinity}] Failure Failure Skip Error
10.9.E13 ((z + zeta)/(z - zeta))^((1)/(2)*nu)* BesselJ(nu, ((z)^(2)- (zeta)^(2))^((1)/(2)))=(1)/(Pi)*int(exp(zeta*cos(theta))*cos(z*sin(theta)- nu*theta), theta = 0..Pi)-(sin(nu*Pi))/(Pi)*int(exp(- zeta*cosh(t)- z*sinh(t)- nu*t), t = 0..infinity) (Divide[z + \[zeta],z - \[zeta]])^(Divide[1,2]*\[Nu])* BesselJ[\[Nu], ((z)^(2)- (\[zeta])^(2))^(Divide[1,2])]=Divide[1,Pi]*Integrate[Exp[\[zeta]*Cos[\[Theta]]]*Cos[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}]-Divide[Sin[\[Nu]*Pi],Pi]*Integrate[Exp[- \[zeta]*Cosh[t]- z*Sinh[t]- \[Nu]*t], {t, 0, Infinity}] Failure Failure Skip Error
10.9.E14 ((z + zeta)/(z - zeta))^((1)/(2)*nu)* BesselY(nu, ((z)^(2)- (zeta)^(2))^((1)/(2)))=(1)/(Pi)*int(exp(zeta*cos(theta))*sin(z*sin(theta)- nu*theta), theta = 0..Pi)-(1)/(Pi)*int((exp(nu*t + zeta*cosh(t))+ exp(- nu*t - zeta*cosh(t))*cos(nu*Pi))* exp(- z*sinh(t)), t = 0..infinity) (Divide[z + \[zeta],z - \[zeta]])^(Divide[1,2]*\[Nu])* BesselY[\[Nu], ((z)^(2)- (\[zeta])^(2))^(Divide[1,2])]=Divide[1,Pi]*Integrate[Exp[\[zeta]*Cos[\[Theta]]]*Sin[z*Sin[\[Theta]]- \[Nu]*\[Theta]], {\[Theta], 0, Pi}]-Divide[1,Pi]*Integrate[(Exp[\[Nu]*t + \[zeta]*Cosh[t]]+ Exp[- \[Nu]*t - \[zeta]*Cosh[t]]*Cos[\[Nu]*Pi])* Exp[- z*Sinh[t]], {t, 0, Infinity}] Failure Failure Skip Error
10.9.E15 ((z + zeta)/(z - zeta))^((1)/(2)*nu)* HankelH1(nu, ((z)^(2)- (zeta)^(2))^((1)/(2)))=(1)/(Pi*I)*exp(-(1)/(2)*nu*Pi*I)*int(exp(I*z*cosh(t)+ I*zeta*sinh(t)- nu*t), t = - infinity..infinity) (Divide[z + \[zeta],z - \[zeta]])^(Divide[1,2]*\[Nu])* HankelH1[\[Nu], ((z)^(2)- (\[zeta])^(2))^(Divide[1,2])]=Divide[1,Pi*I]*Exp[-Divide[1,2]*\[Nu]*Pi*I]*Integrate[Exp[I*z*Cosh[t]+ I*\[zeta]*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity}] Failure Failure Skip Error
10.9.E16 ((z + zeta)/(z - zeta))^((1)/(2)*nu)* HankelH2(nu, ((z)^(2)- (zeta)^(2))^((1)/(2)))= -(1)/(Pi*I)*exp((1)/(2)*nu*Pi*I)*int(exp(- I*z*cosh(t)- I*zeta*sinh(t)- nu*t), t = - infinity..infinity) (Divide[z + \[zeta],z - \[zeta]])^(Divide[1,2]*\[Nu])* HankelH2[\[Nu], ((z)^(2)- (\[zeta])^(2))^(Divide[1,2])]= -Divide[1,Pi*I]*Exp[Divide[1,2]*\[Nu]*Pi*I]*Integrate[Exp[- I*z*Cosh[t]- I*\[zeta]*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity}] Failure Failure Skip Error
10.9.E17 BesselJ(nu, z)=(1)/(2*Pi*I)*int(exp(z*sinh(t)- nu*t), t = infinity - Pi*I..infinity + Pi*I) BesselJ[\[Nu], z]=Divide[1,2*Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, Infinity - Pi*I, Infinity + Pi*I}] Failure Failure Skip
Fail
Complex[0.342503927390088, -0.08973210023585859] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.3263028372306598, 4.480608248698951] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-26.41355287980499, 14.935276359740396] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.2663767645899945, 0.9702347233898156] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
10.9#Ex7 HankelH1(nu, z)=(1)/(Pi*I)*int(exp(z*sinh(t)- nu*t), t = - infinity..infinity + Pi*I) HankelH1[\[Nu], z]=Divide[1,Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity + Pi*I}] Failure Failure Skip Error
10.9#Ex8 HankelH2(nu, z)= -(1)/(Pi*I)*int(exp(z*sinh(t)- nu*t), t = - infinity..infinity - Pi*I) HankelH2[\[Nu], z]= -Divide[1,Pi*I]*Integrate[Exp[z*Sinh[t]- \[Nu]*t], {t, - Infinity, Infinity - Pi*I}] Failure Failure Skip Error
10.9.E19 BesselJ(nu, z)=(((1)/(2)*z)^(nu))/(2*Pi*I)*int(exp(t -((z)^(2))/(4*t))*(1)/((t)^(nu + 1)), t = - infinity..(0 +)) BesselJ[\[Nu], z]=Divide[(Divide[1,2]*z)^(\[Nu]),2*Pi*I]*Integrate[Exp[t -Divide[(z)^(2),4*t]]*Divide[1,(t)^(\[Nu]+ 1)], {t, - Infinity, (0 +)}] Error Failure - Error
10.9.E20 BesselJ(nu, z)=(GAMMA((1)/(2)- nu)*((1)/(2)*z)^(nu))/((Pi)^((3)/(2))* I)*int(cos(z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 0..(1 +)) BesselJ[\[Nu], z]=Divide[Gamma[Divide[1,2]- \[Nu]]*(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[3,2])* I]*Integrate[Cos[z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 0, (1 +)}] Error Failure - Error
10.9#Ex9 HankelH1(nu, z)=(GAMMA((1)/(2)- nu)*((1)/(2)*z)^(nu))/((Pi)^((3)/(2))* I)*int(exp(I*z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1 + I*infinity..(1 +)) HankelH1[\[Nu], z]=Divide[Gamma[Divide[1,2]- \[Nu]]*(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[3,2])* I]*Integrate[Exp[I*z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1 + I*Infinity, (1 +)}] Error Failure - Error
10.9#Ex10 HankelH2(nu, z)=(GAMMA((1)/(2)- nu)*((1)/(2)*z)^(nu))/((Pi)^((3)/(2))* I)*int(exp(- I*z*t)*((t)^(2)- 1)^(nu -(1)/(2)), t = 1 - I*infinity..(1 +)) HankelH2[\[Nu], z]=Divide[Gamma[Divide[1,2]- \[Nu]]*(Divide[1,2]*z)^(\[Nu]),(Pi)^(Divide[3,2])* I]*Integrate[Exp[- I*z*t]*((t)^(2)- 1)^(\[Nu]-Divide[1,2]), {t, 1 - I*Infinity, (1 +)}] Error Failure - Error
10.9.E22 BesselJ(nu, x)=(1)/(2*Pi*I)*int((GAMMA(- t)*((1)/(2)*x)^(nu + 2*t))/(GAMMA(nu + t + 1)), t = - I*infinity..I*infinity) BesselJ[\[Nu], x]=Divide[1,2*Pi*I]*Integrate[Divide[Gamma[- t]*(Divide[1,2]*x)^(\[Nu]+ 2*t),Gamma[\[Nu]+ t + 1]], {t, - I*Infinity, I*Infinity}] Failure Failure Skip Error
10.9.E23 BesselJ(nu, z)=(1)/(2*Pi*I)*int((GAMMA(t))/(GAMMA(nu - t + 1))*((1)/(2)*z)^(nu - 2*t), t = - infinity - I*c..- infinity + I*c) BesselJ[\[Nu], z]=Divide[1,2*Pi*I]*Integrate[Divide[Gamma[t],Gamma[\[Nu]- t + 1]]*(Divide[1,2]*z)^(\[Nu]- 2*t), {t, - Infinity - I*c, - Infinity + I*c}] Failure Failure Skip
Fail
Complex[0.342503927390088, -0.08973210023585859] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.3263028372306598, 4.480608248698951] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
Complex[-26.41355287980499, 14.935276359740396] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}
Complex[-0.2663767645899945, 0.9702347233898156] <- {Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
10.9.E24 HankelH1(nu, z)= -(exp(-(1)/(2)*nu*Pi*I))/(2*(Pi)^(2))* int(GAMMA(t)*GAMMA(t - nu)*(-(1)/(2)*I*z)^(nu - 2*t), t = c - I*infinity..c + I*infinity) HankelH1[\[Nu], z]= -Divide[Exp[-Divide[1,2]*\[Nu]*Pi*I],2*(Pi)^(2)]* Integrate[Gamma[t]*Gamma[t - \[Nu]]*(-Divide[1,2]*I*z)^(\[Nu]- 2*t), {t, c - I*Infinity, c + I*Infinity}] Failure Failure Skip Error
10.9.E25 HankelH2(nu, z)=(exp((1)/(2)*nu*Pi*I))/(2*(Pi)^(2))*int(GAMMA(t)*GAMMA(t - nu)*((1)/(2)*I*z)^(nu - 2*t), t = c - I*infinity..c + I*infinity) HankelH2[\[Nu], z]=Divide[Exp[Divide[1,2]*\[Nu]*Pi*I],2*(Pi)^(2)]*Integrate[Gamma[t]*Gamma[t - \[Nu]]*(Divide[1,2]*I*z)^(\[Nu]- 2*t), {t, c - I*Infinity, c + I*Infinity}] Failure Failure Skip Error
10.9.E26 BesselJ(mu, z)*BesselJ(nu, z)=(2)/(Pi)*int(BesselJ(mu + nu, 2*z*cos(theta))*cos((mu - nu)* theta), theta = 0..Pi/ 2) BesselJ[\[Mu], z]*BesselJ[\[Nu], z]=Divide[2,Pi]*Integrate[BesselJ[\[Mu]+ \[Nu], 2*z*Cos[\[Theta]]]*Cos[(\[Mu]- \[Nu])* \[Theta]], {\[Theta], 0, Pi/ 2}] Failure Failure Skip Skip
10.9.E27 BesselJ(nu, z)*BesselJ(nu, zeta)=(2)/(Pi)*int(BesselJ(2*nu, 2*(z*zeta)^((1)/(2))* sin(theta))*cos((z - zeta)* cos(theta)), theta = 0..Pi/ 2) BesselJ[\[Nu], z]*BesselJ[\[Nu], \[zeta]]=Divide[2,Pi]*Integrate[BesselJ[2*\[Nu], 2*(z*\[zeta])^(Divide[1,2])* Sin[\[Theta]]]*Cos[(z - \[zeta])* Cos[\[Theta]]], {\[Theta], 0, Pi/ 2}] Failure Failure Skip Error
10.9.E28 BesselJ(nu, z)*BesselJ(nu, zeta)=(1)/(2*Pi*I)*int(* exp((1)/(2)*t -((z)^(2)+ (zeta)^(2))/(2*t))*BesselI(nu, (z*zeta)/(t))*(1)/(t), t = c - I*infinity..c + I*infinity) BesselJ[\[Nu], z]*BesselJ[\[Nu], \[zeta]]=Divide[1,2*Pi*I]*Integrate[* Exp[Divide[1,2]*t -Divide[(z)^(2)+ (\[zeta])^(2),2*t]]*BesselI[\[Nu], Divide[z*\[zeta],t]]*Divide[1,t], {t, c - I*Infinity, c + I*Infinity}] Error Failure - Error
10.9.E29 BesselJ(mu, x)*BesselJ(nu, x)=(1)/(2*Pi*I)*int((GAMMA(- t)*GAMMA(2*t + mu + nu + 1)*((1)/(2)*x)^(mu + nu + 2*t))/(GAMMA(t + mu + 1)*GAMMA(t + nu + 1)*GAMMA(t + mu + nu + 1)), t = - I*infinity..I*infinity) BesselJ[\[Mu], x]*BesselJ[\[Nu], x]=Divide[1,2*Pi*I]*Integrate[Divide[Gamma[- t]*Gamma[2*t + \[Mu]+ \[Nu]+ 1]*(Divide[1,2]*x)^(\[Mu]+ \[Nu]+ 2*t),Gamma[t + \[Mu]+ 1]*Gamma[t + \[Nu]+ 1]*Gamma[t + \[Mu]+ \[Nu]+ 1]], {t, - I*Infinity, I*Infinity}] Failure Failure Skip Error
10.9.E30 (BesselJ(nu, z))^(2)+ (BesselY(nu, z))^(2)=(8)/((Pi)^(2))*int(cosh(2*nu*t)*BesselK(0, 2*z*sinh(t)), t = 0..infinity) (BesselJ[\[Nu], z])^(2)+ (BesselY[\[Nu], z])^(2)=Divide[8,(Pi)^(2)]*Integrate[Cosh[2*\[Nu]*t]*BesselK[0, 2*z*Sinh[t]], {t, 0, Infinity}] Failure Failure Skip Error
10.11.E1 BesselJ(nu, z*exp(m*Pi*I))= exp(m*nu*Pi*I)*BesselJ(nu, z) BesselJ[\[Nu], z*Exp[m*Pi*I]]= Exp[m*\[Nu]*Pi*I]*BesselJ[\[Nu], z] Failure Failure
Fail
-.3975453294+30.10329939*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}
.3425382206-.8976707513e-1*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}
-.3996358010+30.09969700*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}
-1.326778468-4.481046040*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}
... skip entries to safe data
Fail
Complex[-0.3975452718986143, 30.10329943602099] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[0.34253822069590145, -0.08976707542141499] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-0.3996357209647074, 30.09969706489566] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-397.25907376207414, -7.293217978872368] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
10.11.E2 BesselY(nu, z*exp(m*Pi*I))= exp(- m*nu*Pi*I)*BesselY(nu, z)+ 2*I*sin(m*nu*Pi)*cot(nu*Pi)*BesselJ(nu, z) BesselY[\[Nu], z*Exp[m*Pi*I]]= Exp[- m*\[Nu]*Pi*I]*BesselY[\[Nu], z]+ 2*I*Sin[m*\[Nu]*Pi]*Cot[\[Nu]*Pi]*BesselJ[\[Nu], z] Failure Failure
Fail
59.96664792+53.22883098*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}
-5005.486114+1251.725768*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}
10758.9952-438485.5093*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}
-4.21339-169.756927*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}
... skip entries to safe data
Fail
Complex[59.966647971782265, 53.22883092179323] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5005.486119861246, 1251.7257744468322] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[10758.99323773, -438485.5113105696] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[9.175550013151128, -396.6330304507175] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
10.11.E3 sin(nu*Pi)*HankelH1(nu, z*exp(m*Pi*I))= - sin((m - 1)* nu*Pi)*HankelH1(nu, z)- exp(- nu*Pi*I)*sin(m*nu*Pi)*HankelH2(nu, z) Sin[\[Nu]*Pi]*HankelH1[\[Nu], z*Exp[m*Pi*I]]= - Sin[(m - 1)* \[Nu]*Pi]*HankelH1[\[Nu], z]- Exp[- \[Nu]*Pi*I]*Sin[m*\[Nu]*Pi]*HankelH2[\[Nu], z] Failure Failure
Fail
3216.976842-3084.273397*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}
-5364.683403+219295.3867*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}
-17847467.19-5404443.822*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}
-7000.832672-1549.801603*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}
... skip entries to safe data
Fail
Complex[3216.976837863537, -3084.273404768022] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-5364.6831188620945, 219295.38712307377] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[-1.7847467293085534*^7, -5404443.760123314] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[4.353713736263555, -84.22475855786759] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
10.11.E4 sin(nu*Pi)*HankelH2(nu, z*exp(m*Pi*I))= exp(nu*Pi*I)*sin(m*nu*Pi)*HankelH1(nu, z)+ sin((m + 1)* nu*Pi)*HankelH2(nu, z) Sin[\[Nu]*Pi]*HankelH2[\[Nu], z*Exp[m*Pi*I]]= Exp[\[Nu]*Pi*I]*Sin[m*\[Nu]*Pi]*HankelH1[\[Nu], z]+ Sin[(m + 1)* \[Nu]*Pi]*HankelH2[\[Nu], z] Failure Failure
Fail
-2503.040664+625.9436263*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 1}
5334.577216-219295.7816*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 2}
17848181.49+5401985.686*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)+I*2^(1/2), m = 3}
7008.154936+1947.107340*I <- {nu = 2^(1/2)+I*2^(1/2), z = 2^(1/2)-I*2^(1/2), m = 2}
... skip entries to safe data
Fail
Complex[-2503.040666874715, 625.9436301275297] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[5334.576217054554, -219295.782577897] <- {Rule[m, 2], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[1.7848181319058534*^7, 5401985.77292121] <- {Rule[m, 3], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}
Complex[32720.882533131233, -8309.4971554526] <- {Rule[m, 1], Rule[z, Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Ξ½, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}
... skip entries to safe data
10.11#Ex1