On Some Explicit Formulas for Bernoulli Numbers and Polynomials

Lazhar Fekih-Ahmed (1)

1 ENIT - Ecole Nationale d'Ingénieurs de Tunis

We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of complex order.

Mots clés: Bernoulli numbers; Bernoulli polynomials; Hurwitz zeta function; fractional derivatives

Domaines: Théorie des nombres [math.NT]

Lazhar Fekih-Ahmed. On Some Explicit Formulas for Bernoulli Numbers and Polynomials. 2012. ⟨hal-00603510v2⟩