Explicit upper bounds for the Stirling numbers of the first kind

DOI10.1016/j.jcta.2022.105669zbMath1505.11037OpenAlexW4293027900WikidataQ114162622 ScholiaQ114162622MaRDI QIDQ2169830

José A. Adell

Publication date: 30 August 2022

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2022.105669

zbMATH Keywords

exponential distributionPoisson-binomial distributionStirling numbers of the first kindexplicit upper boundComtet numbers of the first kind

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Probability distributions: general theory (60E05) (zeta (s)) and (L(s, chi)) (11M06)

Cites Work

• Two series expansions for the logarithm of the gamma function involving Stirling numbers and containing only rational coefficients for certain arguments related to \(\pi^{-1}\)
• Completely effective error bounds for Stirling numbers of the first and second kinds via Poisson approximation
• A Charlier-Parseval approach to Poisson approximation and its applications
• The \(r\)-Stirling numbers
• The asymptotic behavior of the Stirling numbers of the first kind
• Asymptotic expansions for the Stirling numbers of the first kind
• Probabilistic methods for obtaining asymptotic formulas for generalized Stirling numbers
• Asymptotics and sharp bounds in the Poisson approximation to the Poisson-binomial distribution
• Explicit expressions and integral representations for the Stirling numbers: a probabilistic approach
• Asymptotic Estimates of Stirling Numbers
• Asymptotic Development of the Stirling Numbers of the First Kind
• Approximation of a Generalized Binomial Distribution
• ASYMPTOTIC ESTIMATES FOR GENERALIZED STIRLING NUMBERS
• New family of Whitney numbers
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