Derivatives of the Hurwitz Zeta Function for Rational Arguments

The article is published in Journal of Computational and Applied Mathematics, 100(1998),201--206.


  • Abstract
  • The functional equation for the Hurwitz Zeta function $\zeta(s, a)$ is used to obtain formulas for derivatives of $\zeta(s, a)$ at negative odd $s$ and rational $a$. For several of these rational arguments, closed form expressions are given in terms of simpler transcendental functions, like the logarithm, the polygamma function, and the Riemann Zeta function.

  • Postscript
  • DVI

  • Please send corrections to Victor S. Adamchik
    Computer Science Department, 
    Carnegie Mellon University, Pittsburgh, PA.