On the Dirichlet's type of Eulerian polynomials

TL;DR

This paper introduces a new class of Eulerian polynomials linked to p-adic q-integrals, derives identities through generating functions, and constructs an L-function interpolating these polynomials at negative integers.

Contribution

It presents a novel Dirichlet's type of Eulerian polynomials, their generating functions, and an associated L-function via Mellin transformation, expanding the theoretical framework.

Findings

Derived new identities for Eulerian polynomials

Constructed an L-function interpolating the polynomials at negative integers

Connected Eulerian polynomials with p-adic q-integrals and Mellin transforms

Abstract

In the present paper, we introduce Eulerian polynomials attached to by using p-adic q-integral on Zp . Also, we give new interesting identities via the generating functions of Dirichlet's type of Eulerian polynomials. After, by applying Mellin transformation to this generating function of Dirichlet' type of Eulerian polynomials, we derive L-function for Eulerian polynomials which interpolates of Dirichlet's type of Eulerian polynomials at negative integers.