title: |
New approach to the complete sum of products of the twisted (h, q)-Bernoulli numbers and polynomials |
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publication: |
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| volume-issue: | 14 - 1 | |
| pages: | 44 - 56 | |
ISSN: |
1402-9251 | |
DOI: |
doi:10.2991/jnmp.2007.14.1.5 (how to use a DOI) | |
author(s): |
Yilmaz SIMSEK, Veli KURT, Daeyeoul KIM |
|
publication date: |
February 2007 |
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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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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |