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Journal of Siberian Federal University. Mathematics & Physics, 2022, Volume 15, Issue 2, Pages 226–235
DOI: https://doi.org/10.17516/1997-1397-2022-15-2-226-235 (Mi jsfu991) 		 
A note on explicit formulas for Bernoulli polynomials

Laala Khaldiab, Farid Bencherifc, Abdallah Derbalb

a University of Bouira, Bouira, Algeria
b EDPNL&HM Laboratory, ENS, Kouba, Algeria
c Faculty of Mathematics, USTHB, LA3C, Algiers, Algeria
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DOI: https://doi.org/10.17516/1997-1397-2022-15-2-226-235
Abstract: For $r\in\left \{1,-1,\frac{1}{2}\right\}$, we prove several explicit formulas for the $n$-th Bernoulli polynomial $B_{n}\left(x \right)$, in which $B_{n}\left(x\right)$ is equal to a linear combination of the polynomials $x^{n}$, $\left(x+r\right)^{n},\ldots,$ $\left(x+rm\right)^{n}$, where $m$ is any fixed positive integer greater than or equal to $n$.
Keywords: Appell polynomial, Bernoulli polynomial, binomial coefficients, combinatorial identities.
Received: 17.04.2021
Received in revised form: 11.10.2021
Accepted: 10.01.2022
Bibliographic databases:
Document Type: Article
UDC: 512.6
Language: English
Citation: Laala Khaldi, Farid Bencherif, Abdallah Derbal, “A note on explicit formulas for Bernoulli polynomials”, J. Sib. Fed. Univ. Math. Phys., 15:2 (2022), 226–235
Citation in format AMSBIB
\Bibitem{KhaBenDer22}
\by Laala~Khaldi, Farid~Bencherif, Abdallah~Derbal
\paper A note on explicit formulas for Bernoulli polynomials
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2022
\vol 15
\issue 2
\pages 226--235
\mathnet{http://mi.mathnet.ru/jsfu991}
\crossref{https://doi.org/10.17516/1997-1397-2022-15-2-226-235}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4416296}
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