Confluent Hypergeometric Functions - 13.28 Physical Applications
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 13.28#Ex1 | f_{1}(\xi) = \xi^{-\frac{1}{2}}V_{\kappa,\frac{1}{2}p}^{(1)}(2\iunit k\xi) |
|
f[1](xi) = (xi)^(-(1)/(2))* (V[kappa ,(1)/(2)*p])^(1)(2*I*k*xi)
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Subscript[f, 1][\[Xi]] == \[Xi]^(-Divide[1,2])* (Subscript[V, \[Kappa],Divide[1,2]*p])^(1)[2*I*k*\[Xi]]
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Failure | Failure | Failed [300 / 300] Result: 1.914213563-.5481881590*I
Test Values: {kappa = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, V[kappa,1/2*p] = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, k = 1}
Result: 3.328427125-1.962401722*I
Test Values: {kappa = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, xi = 1/2*3^(1/2)+1/2*I, V[kappa,1/2*p] = 1/2*3^(1/2)+1/2*I, f[1] = 1/2*3^(1/2)+1/2*I, k = 2}
... skip entries to safe data |
Failed [300 / 300]
Result: Complex[1.914213562373095, -0.5481881585886565]
Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[3.32842712474619, -1.9624017209617517]
Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |
| 13.28#Ex2 | f_{2}(\eta) = \eta^{-\frac{1}{2}}V_{\kappa,\frac{1}{2}p}^{(2)}(-2\iunit k\eta) |
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f[2](eta) = (eta)^(-(1)/(2))* (V[kappa ,(1)/(2)*p])^(2)(- 2*I*k*eta)
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Subscript[f, 2][\[Eta]] == \[Eta]^(-Divide[1,2])* (Subscript[V, \[Kappa],Divide[1,2]*p])^(2)[- 2*I*k*\[Eta]]
|
Failure | Failure | Failed [300 / 300] Result: -1.431851653+1.383663495*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, V[kappa,1/2*p] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, k = 1}
Result: -3.363703307+1.901301586*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I, p = 1/2*3^(1/2)+1/2*I, V[kappa,1/2*p] = 1/2*3^(1/2)+1/2*I, f[2] = 1/2*3^(1/2)+1/2*I, k = 2}
... skip entries to safe data |
Failed [300 / 300]
Result: Complex[-1.4318516525781364, 1.3836634939894803]
Test Values: {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[-3.363703305156273, 1.9013015841945222]
Test Values: {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[f, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[V, κ, Times[Rational[1, 2], p]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |