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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/10.06.03.0015.02









  


  










Input Form





LerchPhi[z, -3, a] == (2 UnitStep[-Re[a]] - 1) ((a^3 (-1 + z)^3 - 3 a^2 (-1 + z)^2 z + 3 a z (-1 + z^2) - z (1 + 4 z + z^2))/(-1 + z)^4) + (UnitStep[-Re[a]] 2 (-((1/(-1 + z)^4) (z (-1 - 3 a^2 (-1 + z)^2 + a^3 (-1 + z)^3 - 4 z - z^2 + 3 a (-1 + z^2) - 3 (-1 + z) (1 - 2 a (-1 + z) + a^2 (-1 + z)^2 + z) Ceiling[Re[a]] + 3 (-1 + a (-1 + z)) (-1 + z)^2 Ceiling[Re[a]]^2 - (-1 + z)^3 Ceiling[Re[a]]^3))) + ((a - Ceiling[Re[a]])^2)^(3/2) (1 - Ceiling[Re[a]] + Floor[Re[a]]) UnitStep[Im[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)





2001-10-29





© 1998- Wolfram Research, Inc.