Explicit expressions and integral representations for the Stirling numbers: a probabilistic approach

DOI10.1186/s13662-019-2337-4zbMath1485.11051OpenAlexW2973909058WikidataQ127229005 ScholiaQ127229005MaRDI QIDQ2670607

José A. Adell, Alberto Lekuona

Publication date: 11 March 2022

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-019-2337-4

zbMATH Keywords

integral representationcharacteristic functionmomentStirling numbersexplicit expressiongeneralized difference operator

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bell and Stirling numbers (11B73) Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) Bernoulli and Euler numbers and polynomials (11B68)

Related Items (3)

Explicit estimates for Comtet numbers of the first kind ⋮ Explicit upper bounds for the Stirling numbers of the first kind ⋮ On the uniqueness conjecture for the maximum Stirling numbers of the second kind

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 \(\pi^{-1}\)
• Some inversion formulas and formulas for Stirling numbers
• On Stirling numbers and Euler sums
• Enumerating some stable partitions involving Stirling and \(r\)-Stirling numbers of the second kind
• On the location of the maximum Stirling number(s) of the second kind
• General convolution identities for Bernoulli and Euler polynomials
• Explicit formulas and combinatorial identities for generalized Stirling numbers
• Some identities involving special numbers and moments of random variables
• Binomial convolution and transformations of Appell polynomials
• On the classes of higher-order Jensen-convex functions and Wright-convex functions. II.
• Integral representations and properties of Stirling numbers of the first kind
• Product of uniform distribution and Stirling numbers of the first kind
• Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
• A Multitude of Expressions for the Stirling Numbers of the First Kind
• Extended stirling polynomials of the second kind and extended Bell polynomials
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