Spivey’s type recurrence relation for Lah-Bell polynomials

The aim of this paper is to derive Spivey’s type recurrence relations for the Lah-Bell polynomials and the [Formula: see text]-Lah-Bell polynomials by utilizing operators [Formula: see text] and [Formula: see text] satisfying the commutation relation [Formula: see text]. Here [Formula: see text] is the ‘multiplication by [Formula: see text]’ operator and [Formula: see text] is the differentiation operator [Formula: see text]. In addition, we obtain Spivey’s type recurrence relation for the [Formula: see text] analogue of [Formula: see text]-Lah-Bell polynomials by some other method without using the operators [Formula: see text] and [Formula: see text].