On Generalized Multi Poly-Euler and Multi Poly-Bernoulli Polynomials

TL;DR

This paper introduces new identities and generalizations of multi poly-Euler and poly-Bernoulli polynomials, expanding their mathematical properties through multiple parameters, symmetrization, and connections to zeta values.

Contribution

It presents novel identities, symmetrized forms, and extended definitions of multi poly-Euler and poly-Bernoulli polynomials using multiple polylogarithms and Hurwitz-Lerch zeta functions.

Findings

Derived new identities for generalized multi poly-Euler polynomials.

Established symmetrized generalizations of these polynomials.

Extended poly-Bernoulli polynomials using multiple polylogarithms and zeta values.

Abstract

In this paper, we establish more identities of generalized multi poly-Euler polynomials with three parameters and obtain a kind of symmetrized generalization of the polynomials. Moreover, generalized multi poly-Bernoulli polynomials are defined using multiple polylogarithm and derive some properties parallel to those of poly-Bernoulli polynomials. These are generalized further using the concept of Hurwitz-Lerch multiple zeta values.