Higher-order frobenius-Euler and poly-Bernoulli mixed type polynomials

TL;DR

This paper introduces higher-order Frobenius-Euler and poly-Bernoulli mixed type polynomials derived from polylogarithmic functions, providing new identities through umbral calculus.

Contribution

It presents novel higher-order mixed polynomials and derives their identities using umbral calculus, expanding the theory of special polynomials.

Findings

Derived identities for the mixed polynomials

Connected these polynomials to polylogarithmic functions

Extended the framework of Frobenius-Euler and poly-Bernoulli polynomials

Abstract

In this paper, we consider higher-order Frobenius-Euler polynomi- als associated with poly-Bernoulli polynomials which are derived from polylogarithmic function. These polynomials are called higher-order Frobenius-Euler and poly-Bernoulli mixed type polynomials. The purpose of this paper is to give various identities of those polynomials arising from umbral calculus.