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LerchPhi






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > Series representations > Generalized power series > Expansions on branch cuts > For Phi^(z,s,a)





http://functions.wolfram.com/10.06.06.0045.01









  


  










Input Form





LerchPhiClassical[z, s, a] \[Proportional] Sum[(z^k (1 + O[a - Subscript[a, 0]]))/ (E^(2 I Pi s Floor[(-(1/(2 Pi))) (Arg[(a + k)/(Subscript[a, 0] + k)] + Arg[-Subscript[a, 0] - k])]) (Subscript[a, 0] + k)^s), {k, 0, n - 1}] + (z^n/(Subscript[a, 0] + n)^s + z^(n + 1) LerchPhiClassical[z, s, Subscript[a, 0] + n + 1]) (1 + O[a - Subscript[a, 0]]) /; -n < Subscript[a, 0] < -n + 1 && Element[n, Integers] && n > 0










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)





2007-05-02





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