This analysis demonstrates recurrence relations for Lah-Bell and r-Lah-Bell polynomials, highlighting the operators involved.
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.
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Kim et al. (2025) studied this question.
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