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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/10.02.20.0040.01









  


  










Input Form





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