An Identity for Generalized Bernoulli Polynomials
Redha Chellal and Farid Bencherif
LA3C, Faculty of Mathematics
Centre for Research Informed Teaching
London South Bank University
Recognizing the great importance of Bernoulli numbers and Bernoulli
polynomials in various branches of mathematics, the present paper develops
two results dealing with these objects. The first one proposes an identity
for the generalized Bernoulli polynomials, which leads to further
generalizations for several relations involving classical Bernoulli
numbers and Bernoulli polynomials. In particular, it generalizes a recent
identity suggested by Gessel. The second result allows the deduction of
similar identities for Fibonacci, Lucas, and Chebyshev polynomials,
as well as for generalized Euler polynomials, Genocchi polynomials,
and generalized numbers of Stirling.
Full version: pdf,
(Concerned with sequences
Received June 30 2020; revised versions received July 19 2020; October 14 2020; November 16 2020; November 18 2020.
Published in Journal of Integer Sequences,
November 24 2020.
Journal of Integer Sequences home page