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Derivatives of the Hurwitz Zeta Function for Rational Arguments
 

Summary: Derivatives of the Hurwitz Zeta Function
for Rational Arguments
JEFF MILLER AND VICTOR S. ADAMCHIK
June 15, 1998
Abstract
The functional equation for the Hurwitz Zeta function i(s; a) is
used to obtain formulas for derivatives of i(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.
1 Introduction
The Hurwitz Zeta function i(s; a), defined as the analytic continuation of
the series
i(s; a) =
1
X
n=0
1
(n + a) s

  

Source: Adamchik, Victor - School of Computer Science, Carnegie Mellon University

 

Collections: Computer Technologies and Information Sciences