A closed form for the Stirling polynomials in terms of the Stirling numbers

DOI10.1515/tmj-2017-0053zbMath1432.11025OpenAlexW3124765623MaRDI QIDQ1689327

Feng Qi, Bai-Ni Guo

Publication date: 12 January 2018

Published in: Tbilisi Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.20944/preprints201703.0055.v1

zbMATH Keywords

Bernoulli numberStirling numberBell polynomialFaà di Bruno's formulaclosed formStirling polynomial

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Bernoulli and Euler numbers and polynomials (11B68) Exponential and trigonometric functions (33B10)

Related Items (7)

A closed form for the Stirling polynomials in terms of the Stirling numbers ⋮ Special values of the Bell polynomials of the second kind for some sequences and functions ⋮ Unnamed Item ⋮ Computation of several Hessenberg determinants ⋮ Some identities related to Eulerian polynomials and involving the Stirling numbers ⋮ Simplifying differential equations concerning degenerate Bernoulli and Euler numbers ⋮ Some symmetric identities involving the Stirling polynomials under the finite symmetric group

Uses Software

• Stirling

Cites Work

• Unnamed Item
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• An explicit formula for Bernoulli polynomials in terms of \(r\)-Stirling numbers of the second kind
• Two closed forms for the Bernoulli polynomials
• Explicit formulas for special values of the Bell polynomials of the second kind and for the Euler numbers and polynomials
• A closed form for the Stirling polynomials in terms of the Stirling numbers
• Some identities and an explicit formula for Bernoulli and Stirling numbers
• Multivariate Stirling polynomials of the first and second kind
• Diagonal recurrence relations, inequalities, and monotonicity related to the Stirling numbers of the second kind
• Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
• A new formula for the Bernoulli numbers of the second kind in terms of the Stirling numbers of the first kind

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