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LerchPhi






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > Series representations > Generalized power series > Expansions at a==a0 > For Phi(z,s,a)





http://functions.wolfram.com/10.06.06.0034.01









  


  










Input Form





LerchPhi[z, s, a] \[Proportional] LerchPhi[z, s, Subscript[a, 0]] + s (Zeta[1 + s, Subscript[a, 0]] - 2 Zeta[1 + s, Subscript[a, 0] + Max[Floor[-Re[Subscript[a, 0]]] + 1, 0]]) (a - Subscript[a, 0]) + ((s (s + 1))/2) (Sum[z^k/((Subscript[a, 0] + k)^2 ((Subscript[a, 0] + k)^2)^(s/2)), {k, 0, Floor[-Re[Subscript[a, 0]]]}] + z^Max[Floor[-Re[Subscript[a, 0]]] + 1, 0] LerchPhi[z, 2 + s, Subscript[a, 0] + Max[Floor[-Re[Subscript[a, 0]]] + 1, 0]]) (a - Subscript[a, 0])^2 + \[Ellipsis] /; (a -> Subscript[a, 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