A new Generating Function of Exponential Polynomials and its Applications to the Related Polynomials and Numbers

TL;DR

This paper introduces a novel generating function for exponential polynomials using an operational computational approach, and explores its applications to geometric polynomials, Bernoulli, and Euler numbers.

Contribution

It presents a new generating function for exponential polynomials and demonstrates its applications to related special polynomials and numbers.

Findings

Derived a new generating function for exponential polynomials

Applied the generating function to geometric polynomials, Bernoulli, and Euler numbers

Provided computational proofs using an operational method

Abstract

In this paper we use computational method based on operational point of view to prove a new generating function of exponential polynomials. We give its applications involving geometric polynomials, Bernoulli and Euler numbers.