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
Type
Resource Types::text::journal::journal article
URL
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.