Explicit formulas for degenerate Bernoulli numbers (Q1356666)

\textit{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 \(\leq m\). 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 \(\beta_m(\lambda)\).