Asymptotics of Chebyshev-Stirling and Stirling numbers of the second kind

TL;DR

This paper derives asymptotic formulas for Chebyshev-Stirling and classical Stirling numbers of the second kind using probabilistic methods, enhancing understanding of their behavior for large parameters.

Contribution

It introduces new asymptotic formulas for Chebyshev-Stirling numbers and extends the probabilistic approach to classical Stirling numbers, providing deeper insights.

Findings

Asymptotic formulas for Chebyshev-Stirling numbers derived

Probabilistic approach applicable to classical Stirling numbers

Enhanced asymptotic analysis for Stirling numbers of the second kind

Abstract

For the Chebyshev-Stirling numbers, a special case of the Jacobi-Stirling numbers, asymptotic formulae are derived in terms of a local central limit theorem. The underlying probabilistic approach also applies to the classical Stirling numbers of the second kind. Thereby a supplement of the asymptotic analysis for these numbers is established.