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variants of this functions
EllipticThetaPrime






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/09.05.06.0016.01









  


  










Input Form





EllipticThetaPrime[1, z, q] == (((6 Sqrt[Pi] I)/(q - 1)^(3/2)) Sum[Binomial[k + 3/2, k] Sum[(((-1)^j Binomial[k, j])/(2 j + 3)) Subscript[p, j, k] (q - 1)^k E^((Pi^2 + 4 z^2)/(4 Log[q])) Sum[(-1)^m E^((m (m + 1) Pi^2)/Log[q]) ((2 m + 1) Pi Cosh[((1 + 2 m) Pi z)/Log[q]] + 2 z Sinh[((1 + 2 m) Pi z)/Log[q]]), {m, 0, Infinity}], {j, 0, k}], {k, 0, Infinity}])/E^(I Pi Floor[-(Arg[q - 1]/(2 Pi))]) /; (Abs[q] < 1 && Abs[q - 1] < 1) && Subscript[c, k] == (-1)^(k - 1)/(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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<cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <sinh /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> m </ci> </apply> <cn type='integer'> 1 </cn> </apply> <pi /> <ci> z </ci> <apply> <power /> <apply> <ln /> <ci> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <and /> <apply> <lt /> <apply> <abs /> <ci> q </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <lt /> <apply> <abs /> <apply> <plus /> <ci> q </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <plus /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> k </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <sum /> <bvar> <ci> m </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> k </ci> </uplimit> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> j </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <ci> m </ci> </apply> <apply> <ci> Subscript </ci> <ci> c </ci> <ci> m </ci> </apply> <apply> <ci> Subscript </ci> <ci> p </ci> <ci> j </ci> <apply> <plus /> <ci> k </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> k </ci> <apply> <ci> SuperPlus </ci> <integers /> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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