Derivative of the odd Mathieu function: Series representations (formula 11.04.06.0005)

MathieuSPrime

$Mathematica Notation$

Mathieu and Spheroidal Functions

MathieuSPrime[a,q,z]

Series representations

Generalized power series

Expansions at q==0

http://functions.wolfram.com/11.04.06.0005.01

Input Form

MathieuSPrime[MathieuCharacteristicB[2, q], q, z] \[Proportional] 2 Cos[2 z] - (1/3) Cos[4 z] q + ((-(1/144)) Cos[2 z] + (1/64) Cos[6 z]) q^2 + ((1/384) Cos[4 z] - Cos[8 z]/2880) q^3 + ((119 Cos[2 z])/1327104 - (19 Cos[6 z])/122880 + Cos[10 z]/221184) q^4 + (-((1373 Cos[4 z])/39813120) + Cos[8 z]/259200 - Cos[12 z]/25804800) q^5 + (-((1003 Cos[2 z])/707788800) + (8941 Cos[6 z])/4246732800 - Cos[10 z]/18579456 + Cos[14 z]/4246732800) q^6 + SeriesData[$CellContext`q, 0, {}, 0, 11, 1]

Standard Form

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MathML Form

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</cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 8941 <sep /> 4246732800 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 18579456 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4246732800 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> </list> <cn type='integer'> 0 </cn> <cn type='integer'> 11 </cn> <cn type='integer'> 1 </cn> </apply> </annotation-xml> </semantics> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Proportional </ci> <apply> <apply> <partialdiff /> <list> <cn type='integer'> 1 </cn> </list> <ci> Se </ci> </apply> <apply> <ci> MathieuCharacteristicB </ci> <cn type='integer'> 2 </cn> 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<apply> <cos /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> </list> <cn type='integer'> 0 </cn> <cn type='integer'> 11 </cn> <cn type='integer'> 1 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2001-10-29