 
Summary: On the Hurwitz Function for Rational Arguments
V. S. Adamchik
Department of Computer Science
Carnegie Mellon University
Pittsburgh, USA
adamchik@cs.cmu.edu
Abstract
Using functional properties of the Hurwitz zeta function and symbolic deriva
tives of the trigonometric functions, the function (2n + 1, p/q) is expressed in
several ways in terms of other mathematical functions and numbers, including in
particular the Glaisher numbers.
2000 Mathematics Subject Classification. Primary 11M35, 33B99. Secondary
11B75, 33E20.
Key Words and Phrases. Riemann zeta function, Hurwitz zeta function, multiple gamma
function, Stirling numbers, Bernoulli numbers, Euler numbers, Glaisher's numbers,
derivatives of the cotangent.
1 Introduction
The Hurwitz zeta function, one of the fundamental transcendental functions, is traditionally
defined (see [3, 4, 15, 17]) by the series
(s, a) =
