A new type of degenerate poly-Euler polynomials

TL;DR

This paper introduces a novel class of degenerate poly-Euler polynomials derived from degenerate polylogarithm functions, highlighting their potential applications in combinatorics and number theory.

Contribution

It presents the first construction of degenerate poly-Euler polynomials using degenerate polylogarithm functions and establishes related combinatorial identities.

Findings

New degenerate poly-Euler polynomials constructed

Several combinatorial identities derived

Potential applications in mathematics highlighted

Abstract

Many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This focus stems from their nascent importance for applications in combinatorics, number theory and in other aspects of applied mathematics. we construct a new type of degenerate poly-Euler polynomials by using the degenerate polylogarithm functions. We also show several combinatorial identities related to this polynomials and numbers.