2007/01/01 by A. P. Raposo, Alvaro Raposo, H. J. Weber +5 · 41 citations
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Classical orthogonal polynomials #Focus (optics) #Hahn polynomials #Mathematical functions and polynomials #Matrix (chemical analysis) #Orthogonal polynomials #Orthogonality #Polynomial #Quantum Mechanics and Non-Hermitian Physics #nucl-th #quant-ph
paper · pdf · doi:10.2478/s11534-007-0018-5
published in Open Physics 5(3) (De Gruyter Open) · RevTex, 38 pages, 2 figures, review
openalex publication_date 2007/01/01 · arxiv created 2007/06/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Abstract We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.