Degenerate Poly‐Lah‐Bell Polynomials and Numbers

Many mathematicians studied “poly” as a generalization of the well‐known special polynomials such as Bernoulli polynomials, Euler polynomials, Cauchy polynomials, and Genocchi polynomials. In this paper, we define the degenerate poly‐Lah‐Bell polynomials arising from the degenerate polyexponential functions which are reduced to degenerate Lah‐Bell polynomials when k = 1. In particular, we call these polynomials the “poly‐Lah‐Bell polynomials” when λ ⟶0. We give their explicit expression, Dobinski‐like formulas, and recurrence relation. In addition, we obtain various algebraic identities including Lah numbers, the degenerate Stirling numbers of the first and second kind, the degenerate poly‐Bell polynomials, the degenerate poly‐Bernoulli numbers, and the degenerate poly‐Genocchi numbers.