Charting the -Askey scheme. III. Verde-Star scheme for
arXiv:2307.06668 · doi:10.1007/978-3-031-69646-6_5
Abstract
Following Verde-Star, Linear Algebra Appl. 627 (2021), we label families of orthogonal polynomials in the Askey scheme together with their hypergeometric representations by three sequences of polynomials in , two of degree 2 and one of degree 4, satisfying certain constraints. Except for the Hermite polynomials, this gives rise to a precise classification and a very simple uniform parametrization of these families together with their limit transitions. This is displayed in a graphical scheme. We also discuss limits from the -case to the case , although this cannot be done in a uniform way.
v2: minor corrections, 16 pages, 2 figures; to appear in "Orthogonal polynomials and special functions", K. Castillo and A.J. Durán (eds.), Springer-Verlag (volume dedicated to the memory of José Carlos Petronilho)