Carlitz-type and other Bernoulli identities
Journal
Journal of Integer Sequences
ISSN
1530-7638
Date Issued
2016-01-07
Author(s)
Pita-Ruiz, Claudio
Type
text::journal::journal article
Abstract
By using an explicit formula for Bernoulli polynomials we obtained in a recent
work (in which Bn (x) is written as a linear combination of the polynomials (x − r)
n
,
r = 1, . . . , K + 1, where K ≥ n), it is possible to obtain Bernoulli polynomial identities
from polynomial-combinatorial identities. Using this approach, we obtain some generalizations and new demonstrations of the 1971 Carlitz identity involving Bernoulli
numbers, and we also obtain some new identities involving Bernoulli polynomials.
work (in which Bn (x) is written as a linear combination of the polynomials (x − r)
n
,
r = 1, . . . , K + 1, where K ≥ n), it is possible to obtain Bernoulli polynomial identities
from polynomial-combinatorial identities. Using this approach, we obtain some generalizations and new demonstrations of the 1971 Carlitz identity involving Bernoulli
numbers, and we also obtain some new identities involving Bernoulli polynomials.