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variants of this functions
Zeta






Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s,a] > Series representations > Asymptotic series expansions > For zeta(+-n,a) by a





http://functions.wolfram.com/10.02.06.0050.01









  


  










Input Form





Zeta[n, a] \[Proportional] (n + 2 a - 1)/(2 a^n (n - 1)) + (1/(n - 1)!) Sum[((2 k + n - 2)!/((2 k)! a^(2 k + n - 1))) BernoulliB[2 k], {k, 1, Infinity}] - Floor[Abs[Arg[a]]/Pi] (((I Pi)^n 2^(n - 1))/(n - 1)!) (I Cot[Pi a] - 1) Sum[((-1)^k k! StirlingS2[n - 1, k] (I Cot[Pi a] + 1)^k)/2^k, {k, 0, n - 1}] + Sum[((k + a)^2)^(-n/2) - (k + a)^(-n), {k, 0, Floor[-Re[a]]}] /; (Abs[a] -> Infinity) && 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





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