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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/10.02.20.0037.01









  


  










Input Form





Derivative[1, 0][Zeta][1 - 2 n, 1/3] == (3^(1/2 - 2 n) (-1)^(n - 1) Pi^(1 - 2 n) PolyGamma[-1 + 2 n, 1/3])/4^n + ((1/2) (3 - 9^n) Derivative[1][Zeta][1 - 2 n])/9^n - ((Sqrt[3] (-1 + 9^n) Pi + 6 Log[3])/(9^n (8 n))) BernoulliB[2 n] /; 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





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