Interpolation function of the genocchi type polynomials

TL;DR

This paper develops generating functions, interpolation functions, and identities for Genocchi type numbers and polynomials with parameters, expanding their theoretical framework and potential applications.

Contribution

It introduces a new approach to Genocchi type numbers and polynomials, including their generating functions, interpolation functions, and multiplication theorems.

Findings

Constructed generating functions for Genocchi type numbers and polynomials.

Established interpolation functions related to these polynomials.

Proved multiplication theorems and derived identities and applications.

Abstract

The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary positive real parameters. We prove multiplication theorem of these polynomials. Furthermore, we give some identities and applications associated with these numbers, polynomials and their interpolation functions.