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JacobiCS






Mathematica Notation

Traditional Notation









Elliptic Functions > JacobiCS[z,m] > Series representations > Generalized power series > Expansions at z==0





http://functions.wolfram.com/09.27.06.0001.02









  


  










Input Form





JacobiCS[z, m] \[Proportional] 1/z + (1/6) (-2 + m) z + (1/360) (-8 + 8 m + 7 m^2) z^3 + ((-32 + 48 m - 78 m^2 + 31 m^3) z^5)/ 15120 + ((-128 + 256 m + 96 m^2 - 224 m^3 + 127 m^4) z^7)/604800 + ((-512 + 1280 m - 1568 m^2 + 1072 m^3 - 1294 m^4 + 511 m^5) z^9)/23950080 + O[z^11]










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> cs </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 6 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> + </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 360 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 8 </mn> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 32 </mn> </mrow> <mo> + </mo> <mrow> <mn> 48 </mn> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mrow> <mn> 78 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 31 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 3 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mn> 15120 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 128 </mn> </mrow> <mo> + </mo> <mrow> <mn> 256 </mn> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> + </mo> <mrow> <mn> 96 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 224 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 127 </mn> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 4 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mn> 604800 </mn> </mfrac> <mo> + </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 512 </mn> </mrow> <mo> + </mo> <mrow> <mn> 1280 </mn> <mo> &#8290; 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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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