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variants of this functions
EllipticTheta




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[3,z,q] > Series representations > q-series > Other q-series representations





http://functions.wolfram.com/09.03.06.0013.01









  


  








Input Form





(EllipticThetaPrime[1, 0, q] EllipticTheta[3, z, q])/ (4 EllipticTheta[3, 0, q] EllipticTheta[1, z, q]) == (1/4) Csc[z] + Sum[(-1)^k (((1 + q^(2 k)) q^k Sin[z])/ (1 - 2 q^(2 k) Cos[2 z] + q^(4 k))), {k, 1, Infinity}] /; Abs[Im[z]] < Im[\[Tau]] && q == E^(I Pi \[Tau])








Standard Form





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MathML Form







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</ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <ci> z </ci> <ci> q </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 3 </cn> <cn type='integer'> 0 </cn> <ci> q </ci> </apply> <apply> <ci> EllipticTheta </ci> <cn type='integer'> 1 </cn> <ci> z </ci> <ci> q </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <csc /> <ci> z </ci> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> q </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> <apply> <power /> <ci> q </ci> <ci> k </ci> </apply> <apply> <sin /> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> q </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> q </ci> <apply> <times /> <cn type='integer'> 4 </cn> <ci> k </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <lt /> <apply> <abs /> <apply> <imaginary /> <ci> z </ci> </apply> </apply> <apply> <imaginary /> <ci> &#964; </ci> </apply> </apply> <apply> <eq /> <ci> q </ci> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <pi /> <ci> &#964; </ci> </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