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LerchPhi




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > Differentiation > Fractional integro-differentiation > With respect to a > For Phi^(z,s,a)





http://functions.wolfram.com/10.06.20.0014.01









  


  








Input Form





D[LerchPhiClassical[z, s, a], {a, \[Alpha]}] == (Gamma[1 - s] a^(-s - \[Alpha]))/Gamma[1 - s - \[Alpha]] + Sum[(z^k HypergeometricPFQRegularized[{1, s}, {1 - \[Alpha]}, -(a/k)])/ k^s, {k, 1, Infinity}]/a^\[Alpha] /; Abs[z] < 1 && Re[s] > 1








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