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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/10.02.06.0013.01









  


  








Input Form





Derivative[1, 0][Zeta][s, a] \[Proportional] (-(1/(s - 1) + Log[a])) Zeta[s, a] + 1/(a^s (2 (s - 1))) + (1/(s - 1)) Sum[BernoulliB[k] Sum[(Pochhammer[s - 1, k]/(j! (k - j)!)) a^(-s + 1 - k), {j, 0, k - 1}], {k, 2, Infinity}] /; 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