A new family of analytic functions defined by means of Rodrigues type formula

TL;DR

This paper introduces a new family of analytic functions defined via Rodrigues type formulas, exploring their properties, recurrence relations, generating functions, examples, and differential equations.

Contribution

It presents a novel class of analytic functions with derived properties, recurrence relations, generating functions, and differential equations, expanding the theoretical framework.

Findings

Derived recurrence relations for the new functions

Established bilinear and bilateral generating functions

Identified differential equations satisfied by the functions

Abstract

In this article, a class of analytic functions is investigated and their some properties are established. Several recurrence relations and various classes of bilinear and bilateral generating functions for these analytic functions are also derived. Examples of some members belonging to this family of analytic functions are given and differential equations satisfied by these functions are also obtained.