An Identity for Generalized Bernoulli Polynomials
Mehbali, M. (2020). An Identity for Generalized Bernoulli Polynomials. Journal of Integer Sequences. Vol. 23 (2020) (20.11.2), pp. 1 - 25.
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.
|Keywords||Bernoulli numbers, Bernoulli polynomials|
|Journal||Journal of Integer Sequences|
|Journal citation||Vol. 23 (2020) (20.11.2), pp. 1 - 25|
|Publisher||University of Waterloo|
|Web address (URL)||https://cs.uwaterloo.ca/journals/JIS/VOL23/Chellal/chellal7.pdf|
|24 Nov 2020|
|Publication process dates|
|Accepted||30 Jun 2020|
|Deposited||04 Nov 2021|
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The paper has been realized jointly with two authors: Redha Chellal and Farid Bencherif, from the Faculty of Mathematics of USTHB, Algiers, Algeria.
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