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RiemannSiegelZ




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RiemannSiegelZ[z] > Series representations > Generalized power series > Expansions at z==i/2+2i k





http://functions.wolfram.com/10.04.06.0007.01









  


  








Input Form





RiemannSiegelZ[z] \[Proportional] ((-1)^k 2^(-1 - 2 k) Pi^(1/4 - k) (2 k)! Zeta[1 + 2 k] Product[2/Sqrt[1 + 4 j + 2 I z], {j, 0, k - 1}] Sqrt[2 I (z - I/2 - 2 I k)] (1 + O[z - I/2 - 2 I k]))/ E^((1/2) LogGamma[1/2 + k]) /; (z -> I/2 + 2 I k) && Element[k, Integers] && k > 0








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