Proceedings of the Japan Academy, Series A, Mathematical Sciences

A note on $q$-Euler and Genocchi numbers

Lee-Chae Jang, Taekyun Kim, and Hong Kyung Pak

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In [1, 2], L. Carlitz constructed a $q$-Eulerian numbers, by using $q$-difference operator. In this paper, we give another constructions of a $q$-Euler numbers, which are different than his $q$-Euler numbers (see [1], [2]). By using our $q$-Euler numbers, we can investigate the relations between $q$-Euler numbers and $q$-extension of Genocchi numbers.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 77, Number 8 (2001), 139-141.

First available in Project Euclid: 23 May 2006

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Zentralblatt MATH identifier

Primary: 11B68: Bernoulli and Euler numbers and polynomials

$q$-Euler number $q$-analogue of Dirichlet's series


Kim, Taekyun; Jang, Lee-Chae; Pak, Hong Kyung. A note on $q$-Euler and Genocchi numbers. Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 8, 139--141. doi:10.3792/pjaa.77.139.

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