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LerchPhi




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > LerchPhi[z,s,a] > Series representations > Generalized power series > Expansions at z==z0 > For Phi(z,s,a)





http://functions.wolfram.com/10.06.06.0019.01









  


  








Input Form





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








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