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Korean Mathematical Society BKMS

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Bull. Korean Math. Soc. 2006; 43(3): 611-617

Printed September 1, 2006

Copyright © The Korean Mathematical Society.

On the alternating sums of powers of consecutive $q$-integers

Seog-Hoon Rim, Taekyun Kim, and Cheon Seoung Ryoo

Kyungpook National University, Jangjon Research Institute for Mathematical Science, Hannam University

Abstract

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In this paper we construct $q$-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the $q$-analogue of alternating sums of powers of consecutive integers due to Euler.

Keywords: Genocchi numbers and polynomials, $q$-Genocchi numbers and polynomials, alternating sums of powers

MSC numbers: 11S80, 11B68

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