Derivative of the odd Mathieu function: Series representations (formula 11.04.06.0008)

MathieuSPrime

$Mathematica Notation$

Mathieu and Spheroidal Functions

MathieuSPrime[a,q,z]

Series representations

Generalized power series

Expansions at q==0

http://functions.wolfram.com/11.04.06.0008.01

Input Form

MathieuSPrime[MathieuCharacteristicB[5, q], q, z] \[Proportional] 5 Cos[5 z] + ((3/16) Cos[3 z] - (7/24) Cos[7 z]) q + (Cos[z]/384 - (65 Cos[5 z])/4608 + (3/448) Cos[9 z]) q^2 + (-(Cos[z]/9216) - (7 Cos[3 z])/24576 + (13 Cos[7 z])/36864 - (11 Cos[11 z])/129024) q^3 + (-(Cos[z]/589824) - Cos[3 z]/49152 + (4015 Cos[5 z])/2080899072 - Cos[9 z]/229376 + (13 Cos[13 z])/18579456) q^4 + (-((5 Cos[z])/42467328) - (457 Cos[3 z])/11098128384 + (25 Cos[5 z])/7077888 + (1157 Cos[7 z])/7134511104 + (55 Cos[11 z])/1783627776 - Cos[15 z]/247726080) q^5 + ((3407 Cos[z])/799065243648 + (49 Cos[3 z])/226492416 - (9145 Cos[5 z])/456608710656 - (7 Cos[7 z])/56623104 - (1273 Cos[9 z])/310747594752 - (13 Cos[13 z])/101921587200 + (17 Cos[17 z])/980995276800) q^6 + SeriesData[$CellContext`q, 0, {}, 0, 11, 1]

Standard Form

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MathML Form

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<apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -9145 <sep /> 456608710656 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -7 <sep /> 56623104 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1273 <sep /> 310747594752 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -13 <sep /> 101921587200 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 17 <sep /> 980995276800 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 17 </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'> 5 </cn> <ci> q </ci> </apply> <ci> q </ci> <ci> z </ci> </apply> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 3 <sep /> 16 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -7 <sep /> 24 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 384 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -65 <sep /> 4608 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 3 <sep /> 448 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1 <sep /> 9216 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -7 <sep /> 24576 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 13 <sep /> 36864 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -11 <sep /> 129024 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -1 <sep /> 589824 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 49152 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 4015 <sep /> 2080899072 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 229376 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 13 <sep /> 18579456 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 13 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -5 <sep /> 42467328 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> -457 <sep /> 11098128384 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 25 <sep /> 7077888 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1157 <sep /> 7134511104 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 55 <sep /> 1783627776 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 11 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 247726080 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 15 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 3407 <sep /> 799065243648 </cn> <apply> <cos /> <ci> $CellContext`z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 49 <sep /> 226492416 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -9145 <sep /> 456608710656 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -7 <sep /> 56623104 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 7 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1273 <sep /> 310747594752 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Rule Form

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

2001-10-29