Generalized Bernoulli numbers and a formula of Lucas

2014/02/12 by Victor H. Moll, V. H. Moll, Moll, V. H. +3
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1402.2993

arxiv created 2014/02/12 · openalex publication_date 2014/02/12 · arxiv updated 2014/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

An overlooked formula of E. Lucas for the generalized Bernoulli numbers is proved using generating functions. This is then used to provide a new proof and a new form of a sum involving classical Bernoulli numbers studied by K. Dilcher. The value of this sum is then given in terms of the Meixner-Pollaczek polynomials.

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