WeierstrassP[z, {Subscript[g, 2], Subscript[g, 3]}] == (Subscript[e, 1] - Subscript[e, 3]) JacobiNS[Sqrt[Subscript[e, 1] - Subscript[e, 3]] z, (Subscript[e, 2] - Subscript[e, 3])/(Subscript[e, 1] - Subscript[e, 3])]^ 2 + Subscript[e, 3]

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <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> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> e </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> e </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mi> ns </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msqrt> <mrow> <msub> <mi> e </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> e </mi> <mn> 3 </mn> </msub> </mrow> </msqrt> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> &#10072; </mo> <mfrac> <mrow> <msub> <mi> e </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> e </mi> <mn> 3 </mn> </msub> </mrow> <mrow> <msub> <mi> e </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> e </mi> <mn> 3 </mn> </msub> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <msub> <mi> e </mi> <mn> 3 </mn> </msub> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <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 /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> JacobiNS </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> e </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29