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variants of this functions
Zeta




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s] > Summation > Infinite summation





http://functions.wolfram.com/10.01.23.0008.01









  


  








Input Form





Sum[((k + 1)!/Pochhammer[a, k]) Zeta[2 + k] z^k, {k, 0, Infinity}] == ((1 - a)/z^2) (-1 + EulerGamma (-2 + a + z) + (2 - a) Log[-z] - (2 - a) PolyGamma[-1 + a]) + (-z)^(1 - a) Gamma[a] PolyGamma[2 - a, -z] /; Abs[z] < 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