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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/10.06.03.0058.01









  


  








Input Form





LerchPhi[z, n, a] == ((1 - (1 - (-1)^n) UnitStep[-Re[a]]) HypergeometricPFQ[{1, Subscript[a, 1], Subscript[a, 2], \[Ellipsis], Subscript[a, n]}, {1 + Subscript[a, 1], 1 + Subscript[a, 2], \[Ellipsis], 1 + Subscript[a, n]}, z])/a^n + UnitStep[-Re[a]] (1 - (-1)^n) z^Floor[-Re[a]] ((z HypergeometricPFQ[{1, Subscript[b, 1], Subscript[b, 2], \[Ellipsis], Subscript[b, n]}, {1 + Subscript[b, 1], 1 + Subscript[b, 2], \[Ellipsis], 1 + Subscript[b, n]}, z])/(a + Floor[-Re[a]] + 1)^n + (UnitStep[Im[a]] (1 + Floor[-Re[a]] + Floor[Re[a]]))/ ((Floor[-Re[a]] + a)^2)^(n/2)) /; Subscript[b, n] == Subscript[a, n] + Floor[-Re[Subscript[a, n]]] + 1 && Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n] == a && Element[n, Integers] && n > 0








Standard Form





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MathML Form







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</ci> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> n </ci> </apply> <ci> a </ci> </apply> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02