Probabilistic degenerate poly-Bell polynomials associated with random variables

Abstract

Let [Formula: see text] be a random variable whose moment generating function exists in a neighbourhood of the origin. The aim of this paper is to study the probabilistic degenerate poly-Bell polynomials associated with the random variable [Formula: see text], arising from the degenerate polyexponential functions, which are probabilistic extensions of degenerate versions of the poly-Bell polynomials. We derive several explicit expressions and some related identities for them. In addition, we consider the special cases that [Formula: see text] is the Bernoulli random variable with probability of success [Formula: see text] or the gamma random variable with shape parameter 1 and scale parameter 1.

Keywords

• Degenerate polyexponential function
• probabilistic degenerate poly-Bell polynomials
• 11B73
• 11B83
• 60-08