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variants of this functions
Zeta




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s,a] > Summation > Infinite summation > Infinite summation > For zeta(s,a)





http://functions.wolfram.com/10.02.23.0007.01









  


  








Input Form





Sum[(((-1)^k (k + 1)! z^k)/Pochhammer[a, k]) Zeta[k + 2, 1/2], {k, 0, Infinity}] == (Gamma[a]/(2 z^2)) ((2 EulerGamma z + (-2 + a) Log[4])/Gamma[-1 + a] + 2^(1 - a) z^(3 - a) ((-2^a) PolyGamma[2 - a, z] + 8 PolyGamma[2 - a, 2 z]))








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