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variants of this functions
EllipticTheta






Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[2,z,q] > Transformations > Transformations and argument simplifications > Argument involving basic arithmetic operations





http://functions.wolfram.com/09.02.16.0005.01









  


  










Input Form





EllipticTheta[2, Pi (1/2 + (-1 + n) z), E^(I Pi \[Tau])]/ EllipticTheta[2, Pi (1/2 + z), E^(I Pi \[Tau])] == Product[EllipticTheta[2, Pi (1/2 + n z + k \[Tau]), E^(I n Pi \[Tau])]/ EllipticTheta[2, Pi (1/2 + k \[Tau]), E^(I n Pi \[Tau])], {k, 1, -1 + n}] Sum[(\[CurlyTheta][k \[Tau], n \[Tau]] E^((n^2 - n - 2 k) I Pi z))/\[CurlyTheta][n z + k \[Tau], n \[Tau]], {k, 1, n - 1}] /; Im[\[Tau]] > 0 && Element[n, Integers] && n >= 1










Standard Form





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MathML Form







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</mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mi> &#977; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mi> k </mi> <mo> &#8290; </mo> <mi> &#964; </mi> </mrow> </mrow> <mo> , </mo> <mrow> <mi> n </mi> <mo> &#8290; </mo> <mi> &#964; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#964; </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <apply> <times /> <pi /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <pi /> <ci> &#964; </ci> </apply> </apply> </apply> <apply> <power /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <apply> <times /> <pi /> <apply> <plus /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <pi /> <ci> &#964; </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </uplimit> <apply> <times /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <apply> <times /> <pi /> <apply> <plus /> <apply> <times /> <ci> n </ci> <ci> z </ci> </apply> <apply> <times /> <ci> k </ci> <ci> &#964; </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> n </ci> <pi /> <ci> &#964; </ci> </apply> </apply> </apply> <apply> <power /> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 2 </cn> <apply> <times /> <pi /> <apply> <plus /> <apply> <times /> <ci> k </ci> <ci> &#964; 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Rule Form





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





2002-12-18