We consider explicit expansions of some elementary and q-functions in basic Fourier series introduced recently by Bustoz and Suslov. Natural q-extensions of the Bernoulli and Euler polynomials, numbers, and the Riemann zeta function are discussed as a by-product. © 2002 Elsevier Science (USA)

In this paper we construct the q-analogue of Barnes's Bernoulli numbers and polynomials of degree 2, for positive even integers, which is an answer to a part of Schlosser's question. For positive odd integers, Schlosser's question is still open. Finally, we will treat the q-analogue of the sums of powers of consecutive integers.

In the vast literature in Analytic Number Theory, one can find systematic and extensive investigations not only of the classical Bernoulli, Euler and Genocchi polynomials and their corresponding numbers, but also of their many generalizations and basic (or q-) extensions. Our main object in this presentation is to introduce and investigate some of the principal generalizations and unifications ...

1 Department of Mathematics and Computer Science, KonKuk University, Chungju 138-70, Republic of Korea 2 Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea 3 Department of Mathematics, Yuvaraja’s College, University of Mysore, Mysore 570# 005, India 4 Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea 5 Department of ...

The Bernoulli–Barnes polynomials are defined as a natural multidimensional extension of 21 the classical Bernoulli polynomials. Many of the properties of the Bernoulli polynomials 22 admit extensions to this new family. A specific expression involving the Bernoulli–Barnes 23 polynomials has recently appeared in the context of self-dual sequences. The work pre24 sented here provides a proof of t...

Recently, Y. He derived several identities of symmetry for Carlitz’s q-Bernoulli numbers and polynomials by working over the complex field and using q-zeta functions and standard techniques. In this paper, we work over the p-adic field and use the p-adic q-integrals on Zp in order to get the results obtained earlier by him. 664 Dae San Kim, Taekyun Kim, Sang-Hun Lee and Jong-Jin Seo