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RiemannSiegelTheta






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/10.03.06.0015.01









  


  










Input Form





RiemannSiegelTheta[z] == (I/4) ((4 k + 1) Log[Pi] - 2 LogGamma[1/2 + k]) + (1/4) (PolyGamma[1/2 + k] - EulerGamma - 2 Log[Pi]) (z + I/2 + 2 I k) - (I/2) (Log[(-(I/2)) (z + I/2 + 2 I k)] + Sum[Log[(-(I/2)) (z + I/2 + 2 I k) - k + j], {j, 0, k - 1}] - (1/4) Sum[(I^j/(2^j (j + 2))) ((-1)^j Zeta[j + 2, 1/2 + k] - Zeta[j + 2]) (z + I/2 + 2 I k)^(2 + j), {j, 0, Infinity}]) /; (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





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