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arXiv · 1307.7687

p-adic Stirling numbers of the second kind

Donald M. Davis
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Abstract

Let S(n,k) denote the Stirling numbers of the second kind. We prove that the p-adic limit of S(p^e a + c, p^e b + d) as e goes to infinity exists for all integers a, b, c, and d. We call the limiting p-adic integer S(p^\infty a + c, p^\infty b + d). When a equiv b mod (p-1) or d \le 0, we express them in terms of p-adic binomial coefficients introduced in a recent paper.

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Donald M. Davis. 2013-07-29. p-adic Stirling numbers of the second kind. https://arxiv.org/abs/1307.7687

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