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variants of this functions
EllipticTheta




Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[1,z,q] > Series representations > q-series > Expansions at q==1





http://functions.wolfram.com/09.01.06.0041.01









  


  








Input Form





EllipticTheta[1, z, q] \[Proportional] (((2 I Sqrt[Pi])/Sqrt[q - 1]) (1 + O[q - 1]) E^((Pi^2 + 4 z^2)/(4 Log[q])) (Sinh[(Pi z)/Log[q]] + O[E^((2 Pi^2)/Log[q]) Sinh[(3 Pi z)/Log[q]]]))/ E^(I Pi Floor[-(Arg[q - 1]/(2 Pi))]) /; Abs[q] < 1








Standard Form





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MathML Form







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Rule Form





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





2007-05-02