Complementary Polynomials From Rodrigues' Representations For Confluent And Hypergeometric Functions And More

TL;DR

This paper introduces simplified generating functions, recursions, and addition formulas for various special polynomials, including Legendre, confluent, hypergeometric, and relativistic Hermite polynomials, expanding their mathematical framework.

Contribution

It presents new closed-form generating functions and recursions for a range of special polynomials, including novel pre-Laguerre polynomials, enhancing their theoretical understanding.

Findings

Simplified closed-form generating functions for multiple polynomials

New recursions and addition formulas derived

Introduction of pre-Laguerre polynomials

Abstract

Complementary polynomials of Legendre polynomials are briefly presented, as well as those for the confluent and hypergeometric functions, relativistic Hermite polynomials and corresponding new pre-Laguerre polynomials. The generating functions are all given in closed form and are much simpler than the standard ones. Some are simply polynomials in two variables. New recursions and addition formulas are derived.