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On Asymptotic Constants Related to Products of Bernoulli Numbers and Factorials

Bernd C. Kellner
  • Mathematisches Institut, Universität Göttingen, Bunsenstr. 3–5, 37073 Göttingen, Germany. E-mail:
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Published Online: 2009-05-07 | DOI: https://doi.org/10.1515/INTEG.2009.009


We discuss the asymptotic expansions of certain products of Bernoulli numbers and factorials, e.g.,

for integers k ≥ 1 and r ≥ 0. Our main interest is to determine exact expressions, in terms of known constants, for the asymptotic constants of these expansions and to show some relations among them.

Keywords.: Asymptotic constants; Glaisher–Kinkelin constant; Bernoulli number; factorials; Gamma function; Riemann zeta function

About the article

Received: 2007-09-24

Accepted: 2009-02-21

Published Online: 2009-05-07

Published in Print: 2009-04-01

Citation Information: Integers, Volume 9, Issue 1, Pages 83–106, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/INTEG.2009.009.

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