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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Abstract

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

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

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148393021

Digital Object Identifier
doi:10.3792/pjaa.77.139

Mathematical Reviews number (MathSciNet)
MR1863659

Zentralblatt MATH identifier
0997.11017

Subjects
Primary: 11B68: Bernoulli and Euler numbers and polynomials

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

Citation

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. https://projecteuclid.org/euclid.pja/1148393021


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References

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