Affiliation:
1. Department of Physics, Colorado School of MinesGolden, CO 80401, USA
Abstract
The Stieltjes constants
have been of interest for over a century, yet their detailed behaviour remains under investigation. These constants appear in the Laurent expansion of the Hurwitz zeta function
about
. We obtain novel single and double summatory relations for
, including single summation relations for
and
, where
a
and
b
are real and
p
and
q
are positive integers. In addition, we obtain new integration formulae for the Hurwitz zeta function and a new expression for the Stieltjes constants
. Portions of the presentation show an intertwining of the theory of the hypergeometric function with that of the Hurwitz zeta function.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
15 articles.
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