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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/10.02.20.0027.01









  


  










Input Form





Derivative[1, 0][Zeta][-4, a] == 24 PolyGamma[-5, -1 + a] - (1/180) (-1 + a) (-386 + 375 a (3 + (-3 + a) a)) + (1/30) a (-1 + a^2 (10 + 3 a (-5 + 2 a))) EulerGamma + (-1 + a)^4 Log[-1 + a] - 4 (-1 + a)^3 Log[Glaisher] - (1/2) (-1 + a)^4 Log[2 Pi] + (1/(12 Pi^4)) (9 (-2 (-1 + a)^2 Pi^2 Zeta[3] + Zeta[5]) + (-25 + 12 EulerGamma) Pi^4 Zeta[-4, a]) + 4 (-1 + a) Derivative[1][Zeta][-3] + Sum[(1/2) (a + k)^4 (2 Log[a + k] - Log[(a + k)^2]), {k, 0, Floor[1 - Re[a]]}]










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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