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RiemannSiegelTheta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RiemannSiegelTheta[z] > Series representations > Generalized power series > Expansions on branch cuts > In the lower half-plane





http://functions.wolfram.com/10.03.06.0023.01









  


  










Input Form





RiemannSiegelTheta[z] == RiemannSiegelTheta[Subscript[z, 0]] - Pi Floor[(1 - 2 I Subscript[z, 0])/4] Floor[Arg[(-I) (z - Subscript[z, 0])]/(2 Pi)] - (I/2) Sum[((-I)^k/(2^k k!)) ((-1)^k PolyGamma[-1 + k, 1/4 + (I Subscript[z, 0])/2] - PolyGamma[-1 + k, 1/4 - (I Subscript[z, 0])/2] + 2 Log[Pi] KroneckerDelta[k - 1]) (z - Subscript[z, 0])^k, {k, 1, Infinity}] /; Element[I Subscript[z, 0], Reals] && I Subscript[z, 0] > 1/2 && !Element[(I Subscript[z, 0])/2, 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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