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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/10.06.06.0043.01









  


  










Input Form





LerchPhi[z, s, a] \[Proportional] (z^n (1 + O[a - Subscript[a, 0]]))/ (I^s E^(I Pi s Floor[(-(1/Pi)) (Arg[(a + n)/(Subscript[a, 0] + n)] + Arg[(-I) (Subscript[a, 0] + n)])]) ((-I) (Subscript[a, 0] + n))^ s) + (Sum[z^k/(-Subscript[a, 0] - k)^s, {k, 0, n - 1}] + z^(n + 1) LerchPhi[z, s, 1 + Subscript[a, 0] + n]) (1 + O[a - Subscript[a, 0]]) /; Re[Subscript[a, 0]] == -n && 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