Journal of Integer Sequences, Vol. 23 (2020), Article 20.11.2

An Identity for Generalized Bernoulli Polynomials

Redha Chellal and Farid Bencherif
LA3C, Faculty of Mathematics

Mohamed Mehbali
Centre for Research Informed Teaching
London South Bank University
United Kingdom


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,    dvi,    ps,    latex    

(Concerned with sequences A000032 A000045 A000129 A001045 A001542 A001906 A002203 A002450 A003499 A005248 A008277 A014551 A052539.)

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.

Return to Journal of Integer Sequences home page