Department of Mathematics, Tokyo Institute of Technology, Meguro, Tokyo, 152-0033 Japan ; Faculty of Mathematics, Kyushu University, Hakozaki, Fukuoka, 812-8581 Japan
Abstract:
We introduce and study a -analogue of the Euler constant via a suitably defined -analogue of the Riemann zeta function. We show, in particular, that the value is irrational. We also present a -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 .