AbstractBeginning 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 [1], Euler [2], Lucas [3], Appell [4], and Hürwitz [5]. 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. Additional informationNotes on contributorsD. H. LehmerDr. Lehmer needs no introduction to readers of the MONTHLY. It is a pleasure to have a contribution from him in these pages. Ed.
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D. H. Lehmer (1988) studied this question.