Geodesic
A note on explicit formulas for Bernoulli polynomials
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 226-235

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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: combinatorial identities.
Mots-clés : Appell polynomial, Bernoulli polynomial, binomial coefficients 
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Laala Khaldi; Farid Bencherif; Abdallah Derbal. A note on explicit formulas for Bernoulli polynomials. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 15 (2022) no. 2, pp. 226-235. http://geodesic.mathdoc.fr/item/JSFU_2022_15_2_a8/