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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/10.06.20.0031.01









  


  








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}] + z^Max[1 - n + Floor[-Re[a]], 0] Sum[(Pochhammer[Max[1 - n + Floor[-Re[a]], 0] + k + 1, n] z^k)/ (n + a + k + Max[1 - n + Floor[-Re[a]], 0])^s, {k, 0, Infinity}] /; Abs[z] < 1 && 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)





2007-05-02