On q-analogues of the Euler constant and Lerch's limit formula

Nobushige Kurokawa, Masato Wakayama

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


We introduce and study a q-analogue γ(q) of the Euler constant via a suitably defined q-analogue of the Riemann zeta function. We show, in particular, that the value γ(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 γ(q).

Original languageEnglish
Pages (from-to)935-943
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number4
Publication statusPublished - Apr 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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