Explicit formulas for degenerate Bernoulli numbers

✍ Scribed by F.T. Howard

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 380 KB
• Volume: 162
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(95)00284-4

✦ Synopsis

The 'degenerate' Bernoulli numbers tim(2) can be defined by means of the exponential generating function x((1 + 2x) 1/~ -1)-1. L. Carlitz proved an analogue of the Staudt-Clausen theorem for these numbers, and he showed that/3m(2) is a polynomial in 2 of degree ~< m. In this paper we find explicit formulas for the coefficients of the polynomial fl"(2), and we give a new proof of the degenerate Staudt-Clausen theorem. New recursion formulas for/3,.(2) are also proved.