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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/10.06.20.0033.01









  


  








Input Form





D[LerchPhi[z, s, a], {z, n}] == z^(Max[Floor[-Re[a]], 0] - n + 1) Sum[StirlingS1[n, j] Binomial[j, p] LerchPhi[z, s - p, a + Max[Floor[-Re[a]], 0] + 1] (-a)^(j - p), {j, 1, n}, {p, 0, j}] + Sum[(Pochhammer[k + 1, n] z^k)/((n + a + k)^2)^(s/2), {k, 0, Floor[-Re[a]] - 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)





2007-05-02