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RamanujanTauTheta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RamanujanTauTheta[z] > Series representations > Generalized power series > Expansions on branch cuts > For the function itself > In the upper half-plane





http://functions.wolfram.com/10.12.06.0005.01









  


  










Input Form





RamanujanTauTheta[z] \[Proportional] RamanujanTauTheta[Subscript[z, 0]] + Pi (6 + Floor[I Subscript[z, 0]]) Floor[Arg[I (z - Subscript[z, 0])]/ (2 Pi)] - (1/2) (2 Log[2 Pi] - PolyGamma[6 - I Subscript[z, 0]] - PolyGamma[6 + I Subscript[z, 0]]) (z - Subscript[z, 0]) - (I/4) (PolyGamma[1, 6 - I Subscript[z, 0]] - PolyGamma[1, 6 + I Subscript[z, 0]]) (z - Subscript[z, 0])^2 + \[Ellipsis] /; (z -> Subscript[z, 0]) && Element[I Subscript[z, 0], Reals] && I Subscript[z, 0] < -6 && !Element[I Subscript[z, 0], Integers]










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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