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RamanujanTauTheta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RamanujanTauTheta[z] > Series representations > Generalized power series > Expansions at z==-6i-i n





http://functions.wolfram.com/10.12.06.0031.01









  


  










Input Form





RamanujanTauTheta[z] == (-(I/2)) Log[(-I) (z + I (6 + n))] + (n Pi)/2 + n Pi Floor[Arg[(-I) (z + I (6 + n))]/(2 Pi)] + I (6 + n) Log[2 Pi] + (I/2) Sum[((-I)^k/k!) ((1 + (-1)^k) PolyGamma[-1 + k, 1] - (-1)^k (PolyGamma[-1 + k, 1 + n] + PolyGamma[-1 + k, 12 + n]) - 2 KroneckerDelta[k - 1] Log[2 Pi]) (z + I (6 + n))^k, {k, 0, Infinity}] /; Abs[z + I (6 + n)] < 1 && Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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Rule Form





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2007-05-02





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