New Extension of Unified Family of Apostol-Type of Polynomials and Numbers

TL;DR

This paper introduces a new unified family of Apostol-type polynomials and numbers, exploring their properties and relationships with classical polynomials and combinatorial numbers, expanding the theoretical framework of special functions.

Contribution

It presents a novel unification of Apostol-type polynomials, deriving properties and connections with various classical polynomials and combinatorial numbers.

Findings

Established new properties of the unified Apostol-type polynomials

Derived relationships with Jacobi, Laguerre, Hermite polynomials, and Stirling numbers

Extended the theoretical understanding of generalized special functions

Abstract

The purpose of this paper is to introduce and investigate a new unification of unified family of Apostol-type polynomials and numbers based on results given in [24] and [25]. Also, we derive some properties for these polynomials and obtain some relationships between the Jacobi polynomials, Laguerre polynomials, Hermite polynomials, Stirling numbers and some other types of generalized polynomials.