-Stirling Numbers Associated to Potential Polynomials

Adell, José A. (Universidad de Zaragoza) ; Bényi, Beáta

Resumen: We introduce the -Stirling numbers of the first and second kinds, which are the coefficients of the potential polynomials when we express them in terms of the monomials and the falling factorials, respectively. These numbers include, as particular cases, the partial and complete Bell polynomials, the degenerate and probabilistic Stirling numbers, and the -restricted Stirling numbers, among others. Special attention is devoted to the computation of such numbers. On the one hand, a recursive formula is provided. On the other hand, we can compute Stirling numbers of one kind in terms of the other, with the help of the classical Stirling numbers.

Idioma: Inglés

DOI: 10.1556/012.2025.04341

Año: 2025

Publicado en: STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA 62, 4 (2025), 382-398
ISSN: 0081-6906

Tipo y forma: Article (Published version)

Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)