On Combinatorial Properties of the degenerate Krawtchouk Appell polynomials

TL;DR

This paper introduces and explores combinatorial properties of degenerate Krawtchouk Appell polynomials, revealing their connections with Stirling numbers, operators, and Bell polynomials.

Contribution

It presents a new class of polynomials and investigates their combinatorial properties and relationships with classical mathematical objects.

Findings

Established combinatorial properties of the new polynomial class.

Connected the polynomials with Stirling numbers and Bell polynomials.

Analyzed the role of scaling and translation operators in these polynomials.

Abstract

The foremost aim of this study is to introduce and study several combinatorial properties and highlight specific aspects of a new class of polynomials sequences known as degenerate Krawtchouk Appell polynomials associated with the degenerate Pascal measure. As applications, the connection that exists between brand-new polynomials, Stirling numbers, scaling operator, translation operator and the orthogonal Bell polynomials has been investigated.