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variants of this functions
SiegelTheta




Mathematica Notation

Traditional Notation









Elliptic Functions > SiegelTheta[{{m1,1,...,m1,r},...,{mr,1,...,mr,r}},{s1,...,sr}] > Primary definition





http://functions.wolfram.com/09.58.02.0001.01









  


  








Input Form





SiegelTheta[{{Subscript[m, 1, 1], \[Ellipsis], Subscript[m, 1, r]}, \[Ellipsis], {Subscript[m, r, 1], \[Ellipsis], Subscript[m, r, r]}}, {Subscript[s, 1], \[Ellipsis], Subscript[s, r]}] == Sum[\[Ellipsis] Sum[Exp[I Pi (n \[CenterDot] \[CapitalOmega] \[CenterDot] n + 2 n \[CenterDot] s)], {Subscript[n, r], -Infinity, Infinity}], {Subscript[n, 1], -Infinity, Infinity}] /; \[CapitalOmega] == {{Subscript[m, 1, 1], \[Ellipsis], Subscript[m, 1, r]}, \[Ellipsis], {Subscript[m, r, 1], \[Ellipsis], Subscript[m, r, r]}} && s == {Subscript[s, 1], \[Ellipsis], Subscript[s, r]} && n = {Subscript[n, 1], \[Ellipsis], Subscript[n, r]}








Standard Form





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MathML Form







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</mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> n </mi> <mn> 1 </mn> </msub> <mo> = </mo> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <mo> &#8230; </mo> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <msub> <mi> n </mi> <mi> r </mi> </msub> <mo> = </mo> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> </mrow> <mi> &#8734; </mi> </munderover> <msup> <mi> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> n </mi> <mo> &#183; </mo> <mi> &#937; </mi> <mo> &#183; </mo> <mi> n </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> n </mi> <mo> &#183; </mo> <mi> s </mi> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> &#937; </mi> <mo> &#63449; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> { </mo> <mrow> <msub> <mi> m </mi> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> </msub> <mo> , </mo> <mo> &#8230; 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</ci> <list> <list> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> <ci> r </ci> </apply> </list> <list> <ci> &#8230; </ci> <ci> &#8230; </ci> <ci> &#8230; </ci> </list> <list> <apply> <ci> Subscript </ci> <ci> m </ci> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <ci> r </ci> <ci> r </ci> </apply> </list> </list> <list> <apply> <ci> Subscript </ci> <ci> s </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> s </ci> <ci> r </ci> </apply> </list> </apply> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <ci> &#8230; </ci> <apply> <sum /> <bvar> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> r </ci> </apply> </bvar> <lowlimit> <apply> <times /> <cn type='integer'> -1 </cn> <infinity /> </apply> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <pi /> <apply> <plus /> <apply> <ci> CenterDot </ci> <ci> n </ci> <ci> &#937; </ci> <ci> n </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> CenterDot </ci> <ci> n </ci> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <eq /> <ci> &#937; </ci> <list> <list> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <cn type='integer'> 1 </cn> <ci> r </ci> </apply> </list> <ci> &#8230; </ci> <list> <apply> <ci> Subscript </ci> <ci> m </ci> <ci> r </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> m </ci> <ci> r </ci> <ci> r </ci> </apply> </list> </list> </apply> <apply> <eq /> <ci> s </ci> <list> <apply> <ci> Subscript </ci> <ci> s </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> s </ci> <ci> r </ci> </apply> </list> </apply> <ci> n </ci> </apply> </apply> <list> <apply> <ci> Subscript </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> n </ci> <ci> r </ci> </apply> </list> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02