2025/11/16 by Kim, Taekyun, Kim, Dae San
#11B73 #11B83 #47N99 #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2511.12433
This paper addresses the unnatural appearance of the two-variable degenerate Fubini polynomials in a recently derived Spivey-type recurrence relation for the fully degenerate Bell polynomials. To solve this, we introduce a new family of polynomial which we also call the fully degenerate Bell polynomials, along with their two-variable counterparts. Our main contribution is the derivation of natural Spivey-type recurrence relations using operator methods. We extend these results to the r-counterparts, the fully degenerate r-Bell polynomials providing Dobinski-like, finite sum, operator expressions, and Spivey-type recurrence relations for all the new polynomials.