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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/10.06.03.0014.02









  


  








Input Form





LerchPhi[z, -n, a] == (1 - (1 - (-1)^n) UnitStep[-Re[a]]) (a^n + Sum[Binomial[n, j] PolyLog[-j, z] a^(n - j), {j, 0, n}]) + UnitStep[-Re[a]] (1 - (-1)^n) z^Floor[-Re[a]] (z ((a + Floor[-Re[a]] + 1)^n + Sum[Binomial[n, j] PolyLog[-j, z] (a + Floor[-Re[a]] + 1)^(n - j), {j, 0, n}]) + UnitStep[Im[a]] (1 + Floor[-Re[a]] + Floor[Re[a]]) ((Floor[-Re[a]] + a)^2)^(n/2)) /; 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)





2001-10-29