The aim of this paper is to derive Spivey's type recurrence relations for the Lah-Bell polynomials and the r-Lah-Bell polynomials by utilizing operators X and D satisfying the commutation relation DX−XD=1. Here X is the 'multiplication by x' operator and D is the differentiation operator D=ddx. In addition, we obtain Spivey's type recurrence relation for the λ analogue of r-Lah-Bell polynomials by some other method without using the operators X and D.
Kim et al. (Thu,) studied this question.