A new approach to Bernoulli polynomials. (English) Zbl 0663.10009

Lehmer, D. H.

Am. Math. Mon. 95, No. 10, 905-911 (1988).

Author’s abstract: “Beginning with Jacob Bernoulli’s discovery before 1705 of the polynomials that bear his name, there have been five approaches to the theory of Bernoulli polynomials. These can be associated with the names of Bernoulli, Euler (1738), Lucas (1891), Appell (1882), and Hurwitz (personal communication via George Pólya). Each mathematician chose to define the Bernoulli polynomials in a different way, and from his definition derived as theorems one or more of the four other definitions. The present article introduces a sixth definition from which the other five are derived.

Reviewer: L.Skula

MSC:

11B39	Fibonacci and Lucas numbers and polynomials and generalizations
05A99	Enumerative combinatorics

Keywords:

umbral calculus; Appell sequences; Bernoulli polynomials