A $(p,q)$-Analogue of Poly-Euler Polynomials and Some Related Polynomials

TL;DR

This paper introduces a new class of poly-Euler polynomials using a $(p,q)$-analogue framework, generalizing existing poly-Euler and related polynomials through combinatorial identities and interrelations.

Contribution

It presents the first $(p,q)$-analogue of poly-Euler polynomials, expanding the $q$-analogue concept and establishing connections with poly-Bernoulli and poly-Cauchy polynomials.

Findings

Derived combinatorial identities for the new polynomials

Established relations with $(p,q)$-poly-Bernoulli and poly-Cauchy polynomials

Generalized classical poly-Euler polynomials through $(p,q)$-parameters

Abstract

In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give several combinatorial identities and properties of these new polynomials. Moreover, we show some relations with the $(p,q)$-poly-Bernoulli polynomials and $(p,q)$-poly-Cauchy polynomials. The $(p,q)$-analogues generalize the well-known concept of the $q$-analogue.