Derivative of the odd Mathieu function: Differential equations (formula 11.04.13.0007)

MathieuSPrime

$Mathematica Notation$

Mathieu and Spheroidal Functions

MathieuSPrime[a,q,z]

Differential equations

Ordinary linear differential equations and wronskians

For the direct function itself

http://functions.wolfram.com/11.04.13.0007.01

Input Form

z^2 Derivative[2][w][z] - z (-1 + r + 2 s + (4 b q r z^r Sin[2 b z^r])/ (a - 2 q Cos[2 b z^r])) Derivative[1][w][z] + (s (r + s) + b^2 r^2 z^(2 r) (a - 2 q Cos[2 b z^r]) + (4 b q r s z^r Sin[2 b z^r])/(a - 2 q Cos[2 b z^r])) w[z] == 0 /; w[z] == Subscript[c, 1] z^s MathieuSPrime[a, q, b z^r] + Subscript[c, 2] z^s MathieuCPrime[a, q, b z^r]

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02