A new approach to Bernoulli polynomials

Dedicated to Professor Laura Gori on her 70th birthday Abstract: Six approaches to the theory of Bernoulli polynomials are known; these are associated with the names of J. Bernoulli (2) ,L.Euler (4) ,E.Lucas (8) ,P. E. Appell (1) ,A. H¨ urwitz (6) and D. H. Lehmer (7) .I nthis note we deal with a new deter- minantal definition for Bernoulli polynomials recently proposed by F. Costabile (3); in particular, we emphasize some consequent procedures for automatic calculation and re- cover the better known properties of these polynomials from this new definition. Finally, after we have observed the equivalence of all considered approaches, we conclude with a circular theorem that emphasizes the direct equivalence of three of previous approaches.