Several explicit formulae for bernoulli polynomials

Komatsu, Takao; Pita-Ruiz, Claudio

Several explicit formulae for bernoulli polynomials

Journal

Advances in Mathematics of Communications

ISSN

1331-0623

Date Issued

2016-05

Author(s)

Komatsu, Takao

Pita-Ruiz, Claudio

Facultad de Ingeniería - CampCM

Type

text::journal::journal article

URL

https://scripta.up.edu.mx/handle/20.500.12552/4757

https://hrcak.srce.hr/file/232446

Abstract

A generalized Stirling numbers of the second kind Sa,b (p, k), in-volved in the expansion (an + b)p =∑p k=0k!Sa,b (p, k)(n k), where a ≠ 0, b are complex numbers, have studied in [16]. In this paper, we show that Bernoulli polynomials Bp(x) can be written in terms of the numbers S1,x (p, k), and then use the known results for S1,x (p, k) to obtain several new explicit formulas, recurrences and generalized recurrences for Bernoulli numbers and polynomials. © 2023, American Institute of Mathematical Sciences. All rights reserved.