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MathieuSPrime






Mathematica Notation

Traditional Notation









Mathieu and Spheroidal Functions > MathieuSPrime[a,q,z] > Series representations > Generalized power series > Expansions at q==0





http://functions.wolfram.com/11.04.06.0009.01









  


  










Input Form





MathieuSPrime[MathieuCharacteristicB[6, q], q, z] \[Proportional] 6 Cos[6 z] + ((1/5) Cos[4 z] - (2/7) Cos[8 z]) q + ((1/320) Cos[2 z] - (111 Cos[6 z])/9800 + (5/896) Cos[10 z]) q^2 + (-((163 Cos[4 z])/784000) + (257 Cos[8 z])/1097600 - Cos[12 z]/16128) q^3 + (-((233 Cos[2 z])/50176000) + (286737 Cos[6 z])/98344960000 - (239 Cos[10 z])/94832640 + Cos[14 z]/2211840) q^4 + (-((256941 Cos[4 z])/983449600000) + (170407 Cos[8 z])/18587197440000 + (41 Cos[12 z])/2528870400 - Cos[16 z]/425779200) q^5 + (-((152641 Cos[2 z])/62940774400000) + (8712317791 Cos[6 z])/ 234198687744000000 - (553237 Cos[10 z])/951664508928000 - (31 Cos[14 z])/476872704000 + Cos[18 z]/108999475200) q^6 + SeriesData[$CellContext`q, 0, {}, 0, 11, 1]










Standard Form





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MathML Form







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<msup> <mi> q </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 152641 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 62940774400000 </mn> </mfrac> </mrow> <mo> + </mo> <mfrac> <mrow> <mn> 8712317791 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 234198687744000000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 553237 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 951664508928000 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 31 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 14 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 476872704000 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 18 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 108999475200 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> q </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> &#8289; </mo> <mo> ( </mo> <msup> <mi> q </mi> <mn> 11 </mn> </msup> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> SeriesData </ci> <ci> $CellContext`q </ci> <cn type='integer'> 0 </cn> <list> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 5 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -2 <sep /> 7 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 320 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -111 <sep /> 9800 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 5 <sep /> 896 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -163 <sep /> 784000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 257 <sep /> 1097600 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 16128 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -233 <sep /> 50176000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 286737 <sep /> 98344960000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -239 <sep /> 94832640 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2211840 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -256941 <sep /> 983449600000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 170407 <sep /> 18587197440000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 41 <sep /> 2528870400 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 425779200 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -152641 <sep /> 62940774400000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> 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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'> 6 </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'> 6 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 5 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -2 <sep /> 7 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 320 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -111 <sep /> 9800 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 5 <sep /> 896 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -163 <sep /> 784000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 257 <sep /> 1097600 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 16128 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -233 <sep /> 50176000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 286737 <sep /> 98344960000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -239 <sep /> 94832640 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2211840 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -256941 <sep /> 983449600000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 170407 <sep /> 18587197440000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 41 <sep /> 2528870400 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 12 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -1 <sep /> 425779200 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 16 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> -152641 <sep /> 62940774400000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 8712317791 <sep /> 234198687744000000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 6 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -553237 <sep /> 951664508928000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -31 <sep /> 476872704000 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 14 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 108999475200 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 18 </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





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