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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 upper half-plane





http://functions.wolfram.com/10.03.06.0026.01









  


  










Input Form





RiemannSiegelTheta[z] \[Proportional] RiemannSiegelTheta[Subscript[z, 0]] + Pi Floor[Arg[I (z - Subscript[z, 0])]/(2 Pi)] Floor[(1 + 2 I Subscript[z, 0])/4] - (1/4) (2 Log[Pi] - PolyGamma[1/4 - (I Subscript[z, 0])/2] - PolyGamma[1/4 + (I Subscript[z, 0])/2]) (z - Subscript[z, 0]) - (I/16) (PolyGamma[1, 1/4 - (I Subscript[z, 0])/2] - PolyGamma[1, 1/4 + (I Subscript[z, 0])/2]) (z - Subscript[z, 0])^2 + O[(z - Subscript[z, 0])^3] /; 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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