Dirichlet's type of twisted Eulerian polynomials in connection with Eulerian-L-function

TL;DR

This paper introduces Dirichlet's type twisted Eulerian polynomials using p-adic integrals, derives new identities, and defines a twisted Eulerian-L-function that interpolates these polynomials at negative integers.

Contribution

It presents a novel approach to twisted Eulerian polynomials via p-adic integrals and introduces a new L-function connecting these polynomials with complex analysis.

Findings

Derived new identities for twisted Eulerian polynomials

Defined a twisted Eulerian-L-function interpolating at negative integers

Connected polynomial theory with p-adic and complex analysis

Abstract

In the present paper, we effect Dirichlet's type of twisted Eulerian polynomials by using p-adic fermionic q-integral on the p-adic integer ring. Also, we introduce some new interesting identities for them. As a result of them, by using contour integral on the generating function of Dirichlet's type of twisted Eulerian polynomials and so we define twisted Eulerian-L-function which interpolates of Dirichlet's type of Eulerian polynomials at negative integers which we state in this paper.