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).
All Science Journal Classification (ASJC) codes
- Applied Mathematics