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RiemannSiegelTheta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > RiemannSiegelTheta[z] > Differentiation > Fractional integro-differentiation





http://functions.wolfram.com/10.03.20.0004.01









  


  










Input Form





D[RiemannSiegelTheta[z], {z, \[Alpha]}] == z^(1 - \[Alpha]) Sum[1/(2 k Gamma[2 - \[Alpha]]) - (1/(1 + 4 k)) (Hypergeometric2F1Regularized[1, 1, 2 - \[Alpha], (2 I z)/(1 + 4 k)] + Hypergeometric2F1Regularized[1, 1, 2 - \[Alpha], -((2 I z)/(1 + 4 k))]), {k, 1, Infinity}] - ((Log[Pi] + EulerGamma) z^(1 - \[Alpha]))/(2 Gamma[2 - \[Alpha]]) - z^(1 - \[Alpha]) (Hypergeometric2F1Regularized[1, 1, 2 - \[Alpha], -2 I z] + Hypergeometric2F1Regularized[1, 1, 2 - \[Alpha], 2 I z])










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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