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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/10.06.20.0009.02









  


  








Input Form





D[LerchPhiClassical[z, s, a], {z, n}] == Sum[StirlingS1[n, j] Binomial[j, p] (z^(Max[Floor[-Re[a]], 0] + 1) LerchPhi[z, s - p, a + Max[Floor[-Re[a]], 0] + 1] + Sum[z^k/(a + k)^(s - p), {k, 0, Floor[-Re[a]]}]) (-a)^(j - p), {j, 1, n}, {p, 0, j}]/z^n /; 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)





2001-10-29