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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On $q$-analogues of the Euler constant and Lerch’s limit formula
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by Nobushige Kurokawa and Masato Wakayama
Proc. Amer. Math. Soc. 132 (2004), 935-943
DOI: https://doi.org/10.1090/S0002-9939-03-07025-4
Published electronically: November 13, 2003

Abstract:

We introduce and study a $q$-analogue $\gamma (q)$ of the Euler constant via a suitably defined $q$-analogue of the Riemann zeta function. We show, in particular, that the value $\gamma (2)$ is irrational. We also present a $q$-analogue of the Hurwitz zeta function and establish an analogue of the limit formula of Lerch in 1894 for the gamma function. This limit formula can be regarded as a natural generalization of the formula of $\gamma (q)$.
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Bibliographic Information
  • Nobushige Kurokawa
  • Affiliation: Department of Mathematics, Tokyo Institute of Technology, Meguro, Tokyo, 152-0033 Japan
  • Email: kurokawa@math.titech.ac.jp
  • Masato Wakayama
  • Affiliation: Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka, 812-8581 Japan
  • Email: wakayama@math.kyushu-u.ac.jp
  • Received by editor(s): September 3, 2002
  • Published electronically: November 13, 2003
  • Additional Notes: Work in part supported by Grant-in-Aid for Scientific Research (B) No. 11440010, and by Grant-in-Aid for Exploratory Research No. 13874004, Japan Society for the Promotion of Science
  • Communicated by: Wen-Ching Winnie Li
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 935-943
  • MSC (2000): Primary 11M35, 33D05
  • DOI: https://doi.org/10.1090/S0002-9939-03-07025-4
  • MathSciNet review: 2045407