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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/10.02.23.0006.01









  


  








Input Form





Sum[(z^k/(n + k)) Zeta[2 + k, a], {k, 0, Infinity}] == (EulerGamma + PolyGamma[a])/((n - 1) z) - (PolyGamma[n - 1] Zeta[2 - n, a] + Derivative[1, 0][Zeta][2 - n, a])/z^n + ((n - 2)! Sum[(z^j/(j! (n - j - 2)!)) (PolyGamma[n - j - 1] Zeta[2 + j - n, a - z] + Derivative[1, 0][Zeta][2 + j - n, a - z]), {j, 0, n - 2}])/z^n /; Re[a] > 0 && Element[n, Integers] && n > 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