Congruences and Recurrences for Bernoulli Numbers of Higher Order

Abstract

In particular, B^\0) = B^\ the Bernoulli number of order k, and BJp = Bn, the ordinary Bernoulli number. Note also that B^ = 0 for n > 0. The polynomials B^\z) and the numbers B^ were first defined and studied by Niels Norlund in the 1920s; later they were the subject of many papers by L. Carlitz and others. For the past twenty-five years not much has been… (More)

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