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LerchPhi






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/10.06.20.0013.01









  


  










Input Form





D[LerchPhiClassical[z, s, a], {s, \[Alpha]}] == Sum[(((-s) Log[a + k])^\[Alpha] GammaRegularized[-\[Alpha], 0, (-s) Log[a + k]] z^k)/(a + k)^s, {k, 0, Infinity}]/s^\[Alpha] /; Abs[z] < 1 || (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





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