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LerchPhi






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > Integral representations > Contour integral representations > Contour integral representations > For Phi^(z,s,a)





http://functions.wolfram.com/10.06.07.0004.02









  


  










Input Form





LerchPhiClassical[z, s, a] == (1/(2 Pi I)) Integrate[(Gamma[t] Gamma[1 - t] (Gamma[a - t]/Gamma[1 + a - t])^s)/ (-z)^t, {t, \[Gamma] - I Infinity, \[Gamma] + I Infinity}] /; 0 < \[Gamma] < 1 && Re[a] > \[Gamma] && z != 0 && (Arg[-z] < Pi || 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