New approach to the complete sum of products of the twisted (h, q)-Bernoulli numbers and polynomials

DOI

10.2991/jnmp.2007.14.1.5How to use a DOI?

Abstract

In this paper, by using q-Volkenborn integral[10], the first author[25] constructed new generating functions of the new twisted (h, q)-Bernoulli polynomials and numbers. We define higher-order twisted (h, q)-Bernoulli polynomials and numbers. Using these numbers and polynomials, we obtain new approach to the complete sums of products of twisted (h, q)-Bernoulli polynomials and numbers. p-adic q-Volkenborn integral is used to evaluate summations of the following form: B(h,v) m,w (y1 + y2 + ... + yv, q) = l1, l2, ..., lv 0 l1 + l2 + ... + lv = m m l1, l2, ..., lv v j=1 B (h) lj ,w(yj, q), where B (h) m,w(yj, q) is the twisted (h, q)-Bernoulli polynomials. We also define new identities involving (h, q)-Bernoulli polnomials and numbers.

Copyright

© 2007, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Yilmaz Simsek
AU  - Veli Kurt
AU  - Daeyeoul Kim
PY  - 2007
DA  - 2007/02/01
TI  - New approach to the complete sum of products of the twisted (h, q)-Bernoulli numbers and polynomials
JO  - Journal of Nonlinear Mathematical Physics
SP  - 44
EP  - 56
VL  - 14
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2007.14.1.5
DO  - 10.2991/jnmp.2007.14.1.5
ID  - Simsek2007
ER  -