Stirling numbers and inverse factorial series

2020/12/29 by Khristo N. Boyadzhiev, Boyadzhiev, Khristo N. · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2012.14546

openalex publication_date 2020/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We study inverse factorial series and their relation to Stirling numbers of the first kind. We prove a special representation of the polylogarithm function in terms of series with such numbers. Using various identities for Stirling numbers of the first kind we construct a number of expansions of functions in terms of inverse factorial series where the coefficients are special numbers. These results are used to prove/reprove the asymptotic expansion of some classical functions. We also prove a binomial formula involving inverse factorials.

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