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variants of this functions
Zeta




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s,a] > Series representations > Generalized power series > Expansions on branch cuts > For zeta^(s,a)





http://functions.wolfram.com/10.02.06.0047.01









  


  








Input Form





ZetaClassical[s, a] == Sum[Sum[(Pochhammer[s, j]/((Subscript[a, 0] + k)^j j!)) (a - Subscript[a, 0])^j, {j, 0, Infinity}]/ (E^(2 I Pi s Floor[(-(1/(2 Pi))) (Arg[(a + k)/(Subscript[a, 0] + k)] + Arg[-Subscript[a, 0] - k])]) (Subscript[a, 0] + k)^s), {k, 0, n - 1}] + Sum[(Pochhammer[s, k]/((Subscript[a, 0] + n)^k k!)) (a - Subscript[a, 0])^k, {k, 0, Infinity}]/(Subscript[a, 0] + n)^s + ZetaClassical[s, a + n + 1] /; (a -> Subscript[a, 0]) && -n < Subscript[a, 0] < -n + 1 && Element[n, Integers] && n > 0








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