Abstract

The degenerate Stirling numbers and degenerate Eulerian polynomials are intimately connected to the arithmetic of generalized factorials. In this article we show that these numbers and similar sequences may in fact be expressed as p-adic integrals of generalized factorials. As an application of this identification we deduce systems of congruences which are analogues and generalizations of the Kummer congruences for the ordinary Bernoulli numbers. Keywords: Degenerate weighted Stirling numbers; Degenerate Eulerian polynomials; Partial Stirling numbers; Kummer congruences; p-adic integration 1.

Citations