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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/10.02.20.0023.01









  


  








Input Form





Derivative[1, 0][Zeta][-1, a] == PolyGamma[-2, a - 1] - (1/12) (-13 + 18 a - 6 a^2 - 12 (-1 + a) Log[-1 + a] + 12 Log[Glaisher] + 6 (-1 + a) Log[2 Pi]) + UnitStep[Floor[-Re[a]]] Sum[(a + i) Log[a + i] - (1/2) ((a + i)^2)^(1/2) Log[(a + i)^2], {i, 0, Floor[-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