|
|||||
|
|
On  -analogues of the Euler constant and Lerch's limit formula |
|
| Authors: | Nobushige Kurokawa Masato Wakayama |
| Institution: | 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  . |
| Keywords: | Euler's constant Riemann's zeta function Hurwitz's zeta function $q$-gamma function Lerch's limit formula |
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文 | |