Journal of Nonlinear Mathematical Physics

Volume 14, Issue 1, February 2007, Pages 44 - 56

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

Authors
Yilmaz SIMSEK, Veli KURT, Daeyeoul KIM
Corresponding Author
Yilmaz SIMSEK
Available Online 1 February 2007.
DOI
https://doi.org/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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
14 - 1
Pages
44 - 56
Publication Date
2007/02
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2007.14.1.5How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Yilmaz SIMSEK
AU  - Veli KURT
AU  - Daeyeoul KIM
PY  - 2007
DA  - 2007/02
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  - https://doi.org/10.2991/jnmp.2007.14.1.5
ID  - SIMSEK2007
ER  -