Probabilistic generalization of Spivey-type relation for degenerate Bell polynomials

2025/08/24 by Kim, Taekyun, Kim, Dae San · 2 citations
#11B73 #11B83 #60-08 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.17228

Abstract

Following Spivey's pivotal discovery of a recurrence relation for Bell numbers, significant research has emerged concerning various generalizations of Bell numbers and polynomials. For example, Kim and Kim established a Spivey-type recurrence relation specifically for degenerate Bell and Dowling polynomials. In this paper, we extend this work by deriving a probabilistic generalization of Spivey-type recurrence relations for both degenerate Bell and degenerate r-Bell polynomials.

Citations

• Probabilistic degenerate poly-Bell polynomials associated with random variables
• Recurrence relations for degenerate Bell and Dowling polynomials via Boson operators
• Generalization of Spivey's recurrence relation
• Some identities related to degenerate r-Bell and degenerate Fubini polynomials
• Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)

Cited by

• A Generalized Recurrence for fully degenerate Bell polynomials
• Spivey-type recurrence relation for fully degenerate Bell polynomials

Related

• Generalization of Spivey's recurrence relation
• Spivey's type recurrence relation for degenerate Bell polynomials
• Spivey-type recurrence relation for fully degenerate Bell polynomials
• A Generalized Recurrence for fully degenerate Bell polynomials
• Recurrence relations for degenerate Bell and Dowling polynomials via Boson operators