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WeierstrassP






Mathematica Notation

Traditional Notation









Elliptic Functions > WeierstrassP[z,{g2,g3}] > Series representations > Generalized power series > Expansions at z==0





http://functions.wolfram.com/09.13.06.0001.01









  


  










Input Form





WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] == 1/z^2 + Sum[Subscript[a, k] z^(2 k - 2), {k, 2, Infinity}] /; Subscript[a, 2] == Subscript[g, 2]/20 && Subscript[a, 3] == Subscript[g, 3]/28 && Subscript[a, k] == (3/((2 k + 1) (k - 3))) Sum[Subscript[a, l] Subscript[a, k - l], {l, 2, k - 2}]










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> <mrow> <mi> &#8472; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> ; </mo> <msub> <mi> g </mi> <mn> 2 </mn> </msub> </mrow> <mo> , </mo> <msub> <mi> g </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mfrac> <mo> + </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#10869; </mo> <mfrac> <msub> <mi> g </mi> <mn> 2 </mn> </msub> <mn> 20 </mn> </mfrac> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> &#10869; </mo> <mfrac> <msub> <mi> g </mi> <mn> 3 </mn> </msub> <mn> 28 </mn> </mfrac> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> a </mi> <mi> k </mi> </msub> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <mn> 3 </mn> <mtext> </mtext> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> k </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> l </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mn> 2 </mn> </mrow> </munderover> <mrow> <msub> <mi> a </mi> <mi> l </mi> </msub> <mo> &#8290; </mo> <msub> <mi> a </mi> <mrow> <mi> k </mi> <mo> - </mo> <mi> l </mi> </mrow> </msub> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> WeierstrassP </ci> <ci> z </ci> <list> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> </list> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> k </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 20 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> g </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <cn type='integer'> 28 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> k </ci> <cn type='integer'> -3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> l </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> k </ci> <cn type='integer'> -2 </cn> </apply> </uplimit> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> l </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> l </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29