Original scientific paper

Several explicit formulae for Bernoulli polynomials

Takao Komatsu orcid.org/0000-0001-6204-5368 ; School of Mathematics and Statistics, Wuhan University, Wuhan, China
Claudio de J. Pita Ruiz V. ; Universidad Panamericana, Benito Juárez, Insurgentes Mixcoac,Ciudad de México,Mexico

Abstract

We prove several explicit formulae for the $n$-th Bernoulli polynomial $B_{n}(x)$, in which $B_{n}(x)$ is equal to an affine combination of the polynomials $(x-1)^{n}$, $(x-2)^{n}$, $\ldots$, $(x-k-1)^{n}$, where $k$ is any fixed positive integer greater or equal than $n$.

Keywords

Bernoulli polynomials; binomial coefficients; Bernoulli numbers

Hrčak ID:

157714

URI

https://hrcak.srce.hr/157714

Publication date:

16.5.2016.

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