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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/10.01.23.0009.01









  


  








Input Form





Sum[(z^k/(n + k)) Zeta[2 + k], {k, 0, Infinity}] == (-z^(-n)) (PolyGamma[n - 1] Zeta[2 - n] + Derivative[1][Zeta][2 - n]) + ((n - 2)! Sum[(z^j/(j! (n - j - 2)!)) (PolyGamma[n - j - 1] Zeta[2 + j - n, 1 - z] + Derivative[1, 0][Zeta][2 + j - n, 1 - z]), {j, 0, n - 2}])/z^n /; 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