Derivative of the angular spheroidal function of the second kind: Series representations (formula 11.13.06.0005)

SpheroidalQSPrime

$Mathematica Notation$

Mathieu and Spheroidal Functions

SpheroidalQSPrime[nu,mu,gamma,z]

Series representations

Generalized power series

Expansions at z==0

http://functions.wolfram.com/11.13.06.0005.01

Input Form

SpheroidalQSPrime[\[Nu], \[Mu], \[Gamma], z] \[Proportional] SpheroidalQSPrime[\[Nu], \[Mu], \[Gamma], 0] - (\[Gamma]^2 - \[Mu]^2 + SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]]) SpheroidalQS[\[Nu], \[Mu], \[Gamma], 0] z - (1/2) (-2 + \[Gamma]^2 - \[Mu]^2 + SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]]) SpheroidalQSPrime[\[Nu], \[Mu], \[Gamma], 0] z^2 + (1/6) (\[Gamma]^4 - 2 \[Gamma]^2 (2 + \[Mu]^2) + \[Mu]^2 (8 + \[Mu]^2) + 2 (-3 + \[Gamma]^2 - \[Mu]^2) SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]] + SpheroidalEigenvalue[\[Nu], \[Mu], \[Gamma]]^2) SpheroidalQS[\[Nu], \[Mu], \[Gamma], 0] z^3 + \[Ellipsis] /; (z -> 0)

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