### Abstract

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 language | English |
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Pages (from-to) | 935-943 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 132 |

Issue number | 4 |

Publication status | Published - Apr 1 2004 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*132*(4), 935-943.

**On q-analogues of the Euler constant and Lerch's limit formula.** / Kurokawa, Nobushige; Wakayama, Masato.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 132, no. 4, pp. 935-943.

}

TY - JOUR

T1 - On q-analogues of the Euler constant and Lerch's limit formula

AU - Kurokawa, Nobushige

AU - Wakayama, Masato

PY - 2004/4/1

Y1 - 2004/4/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=1642414336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1642414336&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:1642414336

VL - 132

SP - 935

EP - 943

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -