, Volume 15, Issue 1, pp 51-57
Date: 03 Apr 2008

q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients

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Abstract

A purpose of this paper is to present a systemic study of some families of multiple q-Bernoulli numbers and polynomials by using the multivariate q-Volkenborn integral (= p-adic q-integral) on ℤ p . Moreover, the study of these higher-order q-Bernoulli numbers and polynomials implies some interesting q-analogs of Stirling number identities.

This paper is supported by Jangjeon Research Institute for Mathematical Science (JRIMS-10R-2001).