The generalized Touchard polynomials revisited

DOI10.1016/j.amc.2013.04.010zbMath1301.11028OpenAlexW2026571809MaRDI QIDQ2016353

Matthias Schork, Toufik Mansour

Publication date: 20 June 2014

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2013.04.010

zbMATH Keywords

generating functionBell numberStirling numberTouchard polynomial

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Special sequences and polynomials (11B83) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10)

Related Items (5)

\((p, q)\)-analogues of the generalized Touchard polynomials and Stirling numbers ⋮ On the real-rootedness of generalized Touchard polynomials ⋮ Tsallis \(p,q\)-deformed Touchard polynomials and Stirling numbers ⋮ On \(q\)-deformed generalized Touchard polynomials ⋮ Limit theorems for numbers satisfying a class of triangular arrays

Uses Software

• OEIS

Cites Work

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• Touchard like polynomials and generalized Stirling numbers
• On a new family of generalized Stirling and Bell numbers
• The commutation relation \(xy=qyx+hf(y)\) and Newton's binomial formula
• Derivations and automorphisms on non-commutative power series.
• Bessel summation formulae and operational methods
• Exponential polynomials, Stirling numbers, and evaluation of some gamma integrals
• Generalized shift operators and pseudo-polynomials of fractional order.
• Universal expansion of the powers of a derivation
• A series transformation formula and related polynomials

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