Several formulas for Bernoulli numbers and polynomials
Journal
Advances in Mathematics of Communications
ISSN
1930-5346
1930-5338
Publisher
American Institute of Mathematical Sciences (AIMS)
Date Issued
2023
Author(s)
Type
text::journal::journal article
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.
How to cite
Komatsu, T., Patel, B. K., & Pita-Ruiz, C. (2023). Several formulas for Bernoulli numbers and polynomials. In Advances in Mathematics of Communications (Vol. 17, Issue 3, pp. 522–535). American Institute of Mathematical Sciences (AIMS). https://doi.org/10.3934/amc.2021006