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Zbl 0873.11016
Howard, F.T.
Explicit formulas for degenerate Bernoulli numbers. (English)
[J] Discrete Math. 162, No.1-3, 175-185 (1996). ISSN 0012-365X

{\it L. Carlitz} [Arch. Math. 7, 28-33 (1956; Zbl 0070.04003)] introduced the `degenerate' Bernoulli numbers $\beta_m(\lambda)$ by means of the generating function $$ \frac{x}{(1+ \lambda x)^{1/\lambda}-1} = \sum_{m=0}^\infty \beta_m(\lambda) \frac{x^m}{m!}. $$ He also proved an analogue of the Staudt-Clausen theorem for these numbers, and he showed that $\beta_m(\lambda)$ is a polynomial in $\lambda$ of degree $\le m$. \par In the paper under review the author gives explicit formulas for the coefficients of the polynomial $\beta_m(\lambda)$ and thereby an alternative proof of the Staudt-Clausen theorem, including some new recursion formulas for $\beta_m(\lambda)$.
[H.Müller (Hamburg)]

MSC 2000:: *11B68 Bernoulli numbers, etc.

Keywords: degenerate Bernoulli numbers; generating function; Staudt-Clausen theorem; recursion formulas

Citations: Zbl 0070.04003

Cited in: Zbl 1093.11014

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