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LerchPhi






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > Specific values > Specialized values > For fixed z, a > For Phi(z,s,a)





http://functions.wolfram.com/10.06.03.0059.01









  


  










Input Form





LerchPhi[z, 1, a] == (Hypergeometric2F1[1, a, 1 + a, z] (1 - 2 UnitStep[-Re[a]]))/a + (2 ((z Hypergeometric2F1[1, 1 + a - Ceiling[Re[a]], 2 + a - Ceiling[Re[a]], z])/(1 + a - Ceiling[Re[a]]) + ((1 - Ceiling[Re[a]] + Floor[Re[a]]) UnitStep[Im[a]])/Sqrt[(a - Ceiling[Re[a]])^2]) UnitStep[-Re[a]])/ z^Ceiling[Re[a]]










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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