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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(1,0)(s,a) by a





http://functions.wolfram.com/10.02.06.0014.01









  


  










Input Form





Derivative[1, 0][Zeta][-n, a] \[Proportional] (BernoulliB[n + 1, a] Log[a])/(n + 1) - ((1/2) a^n (n + 1) + BernoulliB[n + 1, a])/(n + 1)^2 + (-1)^n n! Sum[(a^(-1 - k) BernoulliB[2 + k + n])/Pochhammer[1 + k, 2 + n], {k, 0, Infinity}] - (1/(n + 1)) Sum[BernoulliB[k] Sum[((-1)^j a^(1 - k + n) Binomial[n + 1, k])/(k - j), {j, 0, k - 1}], {k, 2, n + 1}] /; Element[n, Integers] && n > 0 && Inequality[-(Pi/2), Less, Arg[a], LessEqual, Pi/2] && (Re[a] -> Infinity)










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)





2002-12-18





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