Several explicit formulae for bernoulli polynomials

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.