2018•arXiv (Cornell University)Open access

A note on degenerate Stirling numbers of the first kind

Taekyun Kim, Dae San Kim

Abstract

Recently, the degenerate Stirling numbers of the first kind were introduced. In this paper, we give some formulas for the degenerate Stirling numbers of the first kind in the terms of the complete Bell polynomials with higher-order harmonic number arguments. Also, we derive an identity connecting the degenerate Stirling numbers of the first kind and the degenerate derangement numbers by using probabilistic method.

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Key concepts: Degenerate energy levels, Stirling numbers of the second kind, Bell polynomials, Stirling number, Stirling engine, Stirling numbers of the first kind, Mathematics, Identity (music)