On a class of polynomials connected to Bell polynomials

TL;DR

This paper investigates a class of polynomials related to Bell polynomials, exploring their explicit forms, properties, and applications, including connections to hyperbolic differential equations and generalizations of classical polynomials.

Contribution

It introduces a new class of polynomials linked to Bell polynomials, providing explicit formulas, recurrence relations, and applications, simplifying existing results.

Findings

Some polynomials have applications in hyperbolic differential equations

Generalizations include Laguerre and Lah polynomials

Results include explicit expressions and simplified proofs

Abstract

In this paper, we study a class of sequences of polynomials linked to the sequence of Bell polynomials. Some sequences of this class have applications on the theory of hyperbolic differential equations and other sequences generalize Laguerre polynomials and associated Lah polynomials. We discuss, for these polynomials, their explicit expressions, relations to the successive derivatives of a given function, real zeros and recurrence relations. Some known results are significantly simplified.