## On $q$-analogues of the Euler constant and Lerch’s limit formula

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- by Nobushige Kurokawa and Masato Wakayama PDF
- Proc. Amer. Math. Soc.
**132**(2004), 935-943 Request permission

## 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 $\gamma (q)$.## References

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## Additional 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