Other approaches for generalized Bernoulli-Euler polynomials and beyond
Hacène Belbachir, Slimane Hadj-Brahim, Mustapha Rachidi

Abstract. In this paper we develop two approaches for studying a large family of generalized Bernoulli-Euler polynomials. For the determinental approach, using Little Fermat's Theorem, we establish a congruence identity and we give an explicit formulas of the generalized Bernoulli-Euler polynomials in terms of the Stirling numbers. The linear recursive approach allows us to formulate some properties of the generalized Bernoulli-Euler numbers and the generalized Bernoulli-Euler polynomials. Moreover, combinatorial formulas for these polynomials are provided

Rend. Mat. Appl. (7) 44 (2023) 211-235; pdf