Mathieu Functions and Hill’s Equation - 28.30 Expansions in Series of Eigenfunctions
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 28.30.E2 | \frac{1}{2\pi}\int_{0}^{2\pi}w_{m}(x)w_{n}(x)\diff{x} = \Kroneckerdelta{m}{n} |
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(1)/(2*Pi)*int(w[m](x)* w[n](x), x = 0..2*Pi) = KroneckerDelta[m, n]
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Divide[1,2*Pi]*Integrate[Subscript[w, m][x]* Subscript[w, n][x], {x, 0, 2*Pi}, GenerateConditions->None] == KroneckerDelta[m, n]
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Failure | Failure | Failed [300 / 300] Result: 5.579736275+11.39643752*I
Test Values: {w[m] = 1/2*3^(1/2)+1/2*I, w[n] = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}
Result: 6.579736275+11.39643752*I
Test Values: {w[m] = 1/2*3^(1/2)+1/2*I, w[n] = 1/2*3^(1/2)+1/2*I, m = 1, n = 2}
... skip entries to safe data |
Failed [300 / 300]
Result: Complex[5.579736267392906, 11.396437515528111]
Test Values: {Rule[m, 1], Rule[n, 1], Rule[Subscript[w, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[6.579736267392906, 11.396437515528111]
Test Values: {Rule[m, 1], Rule[n, 2], Rule[Subscript[w, m], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[w, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |