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RiemannSiegelTheta




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RiemannSiegelTheta[z] > Series representations > Generalized power series > Expansions at z==z0/;z0!=+-i/2+-2i k





http://functions.wolfram.com/10.03.06.0011.01









  


  








Input Form





RiemannSiegelTheta[z] == RiemannSiegelTheta[Subscript[z, 0]] + (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/8) Sum[((1/(j + 2)) ((I^j ((-1)^j Zeta[j + 2, 1/4 + (I Subscript[z, 0])/2] - Zeta[j + 2, 1/4 - (I Subscript[z, 0])/2]))/2^j)) (z - Subscript[z, 0])^(2 + j), {j, 0, Infinity}] /; Subscript[z, 0]^2 != -(1/2 + 2 k)^2 && Element[k, 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)





2001-10-29