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variants of this functions
EllipticTheta






Mathematica Notation

Traditional Notation









Elliptic Functions > EllipticTheta[3,z,q] > Series representations > q-series > Expansions at q==1





http://functions.wolfram.com/09.03.06.0030.01









  


  










Input Form





EllipticTheta[3, z, q] == (((I Sqrt[Pi])/Sqrt[q - 1]) Sum[Binomial[k + 1/2, k] Sum[(((-1)^j Binomial[k, j])/(2 j + 1)) Subscript[p, j, k] (q - 1)^k E^(z^2/Log[q]) (1 + 2 Sum[E^((k^2 Pi^2)/Log[q]) Cosh[(2 k Pi z)/Log[q]], {k, 1, Infinity}]), {j, 0, k}], {k, 0, Infinity}])/ E^(I Pi Floor[3/4 - Arg[q - 1]/(2 Pi)]) /; (Abs[q] < 1 && Abs[q - 1] < 1) && Subscript[c, k] == (-1)^k/(k + 1) && Subscript[p, j, 0] == 1 && Subscript[p, j, k] == (1/k) Sum[(j m - k + m) Subscript[c, m] Subscript[p, j, k - m], {m, 1, k}] && Element[k, Integers] && k > 0










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





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