Analysis of Bell based Euler polynomials and thier application

TL;DR

This paper explores Bell-based Euler polynomials of order α, deriving new formulas and relations using umbral calculus, and investigates their applications and connections to string numbers of the second kind.

Contribution

It introduces new Bell-based Euler polynomial formulas and relations, expanding the theoretical framework and potential applications of these polynomials.

Findings

Derived correlation, summation, and derivative formulas for Bell-based Euler polynomials.

Established relations with string numbers of the second kind.

Presented new formulae using umbral calculus.

Abstract

In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind. Moreover, we drive several important formulae of bell based Euler polynomial by using umbral calculus.