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LerchPhi






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > Integration > Indefinite integration > Involving only one direct function with respect to a > For Phi^(z,s,a)





http://functions.wolfram.com/10.06.21.0006.01









  


  










Input Form





Integrate[a^(\[Alpha] - 1) LerchPhiClassical[z, s, a], a] == (a^\[Alpha]/(\[Alpha] - s)) Sum[(z^k/((a + k)^s/((a + k)/a)^s)) Hypergeometric2F1[s - \[Alpha], s, 1 + s - \[Alpha], -(k/a)], {k, 0, Infinity}]










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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