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LerchPhi






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > Differentiation > Symbolic differentiation > With respect to z > For Phi(z,s,a)





http://functions.wolfram.com/10.06.20.0032.01









  


  










Input Form





D[LerchPhi[z, s, a], {z, n}] == Sum[(Pochhammer[k + 1, n] z^k)/((n + a + k)^2)^(s/2), {k, 0, Floor[-Re[a]] - n}] - Sum[(Pochhammer[k + 1, n] z^k)/ (n + a + k)^s, {k, 0, Max[1 - n + Floor[-Re[a]], 0] - 1}] + n! Gamma[a + n]^s HypergeometricPFQRegularized[ {Subscript[a, 1], Subscript[a, 2], \[Ellipsis], Subscript[a, s], n + 1}, {1 + Subscript[a, 1], 1 + Subscript[a, 2], \[Ellipsis], 1 + Subscript[a, s]}, z] /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, s] == a + n && Element[n, Integers] && n >= 0 && Element[s, Integers] && s > 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





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