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LerchPhi




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/10.06.20.0045.01









  


  








Input Form





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