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MathieuCPrime






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/11.03.06.0004.01









  


  










Input Form





MathieuCPrime[MathieuCharacteristicA[0, q], q, z] \[Proportional] (1/Sqrt[2]) (Sin[2 z] q - (1/8) Sin[4 z] q^2 + ((-(11/64)) Sin[2 z] + (1/192) Sin[6 z]) q^3 + ((29 Sin[4 z])/1152 - Sin[8 z]/9216) q^4 + ((1891 Sin[2 z])/36864 - (55 Sin[6 z])/49152 + Sin[10 z]/737280) q^5 + (-((8941 Sin[4 z])/1179648) + (89 Sin[8 z])/3686400 - Sin[12 z]/88473600) q^6 + (-((1521691 Sin[2 z])/84934656) + (26641 Sin[6 z])/78643200 - (131 Sin[10 z])/424673280 + Sin[14 z]/14863564800) q^7 + ((11239489 Sin[4 z])/4246732800 - (62299 Sin[8 z])/8493465600 + (181 Sin[12 z])/69363302400 - Sin[16 z]/3329438515200) q^8 + ((3664886951 Sin[2 z])/543581798400 - (48249209 Sin[6 z])/407686348800 + (125119 Sin[10 z])/1331775406080 - (239 Sin[14 z])/15220290355200 + Sin[18 z]/958878292377600) q^9 + (-((7785932591 Sin[4 z])/7827577896960) + (153642299 Sin[8 z])/ 59929893273600 - (226201 Sin[12 z])/284112086630400 + (61 Sin[16 z])/862990463139840 - Sin[20 z]/345196185255936000) q^10 + SeriesData[$CellContext`q, 0, {}, 1, 11, 1])










Standard Form





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MathML Form







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<mfrac> <mrow> <mn> 153642299 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 479439146188800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 226201 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 3409345039564800 </mn> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 61 </mn> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 13807847410237440 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 20 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mn> 6903923705118720000 </mn> </mfrac> <mo> - </mo> <mfrac> <mn> 233552934751 </mn> <mn> 217432719360000 </mn> </mfrac> 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<cn type='rational'> -1 <sep /> 7372800 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 10 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='rational'> -36919 <sep /> 5308416 </cn> <apply> <times /> <cn type='rational'> 8941 <sep /> 4718592 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> -89 <sep /> 29491200 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 8 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 1061683200 </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'> 1521691 <sep /> 169869312 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> $CellContext`z </ci> </apply> </apply> </apply> 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Rule Form





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





2001-10-29





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