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variants of this functions
Zeta




Mathematica Notation

Traditional Notation









Zeta Functions and Polylogarithms > Zeta[s,a] > Differentiation > Low-order differentiation > With respect to s > For zeta(s,a) > Derivatives at negarive integer points





http://functions.wolfram.com/10.02.20.0043.01









  


  








Input Form





Derivative[1, 0][Zeta][-n, a] + (-1)^n Derivative[1, 0][Zeta][-n, 1 - a] == ((Pi I)/(n + 1)) BernoulliB[n + 1, a] + ((n!/(2 Pi)^n) PolyLog[n + 1, E^(2 Pi I a)])/E^(Pi I (n/2)) /; Inequality[-(Pi/2), Less, Arg[a], LessEqual, Pi/2] && Inequality[-(Pi/2), Less, Arg[1 - a], LessEqual, Pi/2] && 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