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LerchPhi






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > Series representations > Generalized power series > Expansions at z==z0 > For Phi^(z,s,a)





http://functions.wolfram.com/10.06.06.0023.01









  


  










Input Form





LerchPhiClassical[z, s, a] == Sum[(1/(Subscript[z, 0]^k k!)) Sum[StirlingS1[k, j] Binomial[j, p] (Subscript[z, 0]^(Max[Floor[-Re[a]], 0] + 1) LerchPhi[Subscript[z, 0], s - p, a + Max[Floor[-Re[a]], 0] + 1] + Sum[Subscript[z, 0]^i/(a + i)^(s - p), {i, 0, Floor[-Re[a]]}]) (-a)^(j - p) (z - Subscript[z, 0])^k, {j, 1, k}, {p, 0, j}], {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)





2007-05-02





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