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LerchPhi




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/10.06.20.0015.01









  


  








Input Form





D[LerchPhi[z, s, a], z] == z^Max[Floor[-Re[a]], 0] ((-a) LerchPhi[z, s, a + Max[Floor[-Re[a]], 0] + 1] + LerchPhi[z, s - 1, a + Max[Floor[-Re[a]], 0] + 1]) + Sum[((k + 1) z^k)/((a + k + 1)^2)^(s/2), {k, 0, Floor[-Re[a]] - 1}]








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