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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/10.02.20.0045.01









  


  








Input Form





Derivative[1, 0][Zeta][s, a] == Derivative[1, 0][Zeta][s, a - Floor[Re[a]]] + (Sign[Re[a]]/2) Sum[Log[(1/2 + ((1 - 2 a)/2) Sign[Re[a]] + k)^2]/ ((1/2 + ((1 - 2 a)/2) Sign[Re[a]] + k)^2)^(s/2), {k, 0, Abs[Floor[Re[a]]] - 1}] /; !Element[a, Integers]








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