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

2018/03/28 by Hans J. Weber, Weber, H. J.
Mathematics · Physics and Astronomy · #33C45 #Advanced Mathematical Identities #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Mathematical functions and polynomials #Nuclear Theory (nucl-th) #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.1803.10706

openalex publication_date 2018/03/28 · openalex created_date 2018/04/06 · openalex updated_date 2026/07/28

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.

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