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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
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
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
Linking options:
https://www.mathnet.ru/eng/jsfu991 https://www.mathnet.ru/eng/jsfu/v15/i2/p226
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Abstract page: | 89 | Full-text PDF : | 113 | References: | 25 |
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