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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/10.02.20.0035.01









  


  








Input Form





Derivative[1, 0][Zeta][1 - 2 n, 1/6] == -(((9^n - 1) (2^(2 n - 1) + 1) BernoulliB[2 n] Pi)/ (Sqrt[3] 6^(2 n - 1) 8 n)) + ((3^(2 n - 1) - 1) BernoulliB[2 n] Log[2])/ (6^(2 n - 1) 4 n) + ((2^(2 n - 1) - 1) BernoulliB[2 n] Log[3])/ (6^(2 n - 1) 4 n) - ((-1)^n (2^(2 n - 1) + 1) PolyGamma[2 n - 1, 1/3])/ (2 Sqrt[3] (12 Pi)^(2 n - 1)) + ((2^(2 n - 1) - 1) (3^(2 n - 1) - 1) Derivative[1][Zeta][-2 n + 1])/(2 6^(2 n - 1)) /; 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