Hypergeometric orthogonal polynomials of Jacobi type

• DOI: 10.48550/arxiv.2401.14715
• Publication Date: 2024-01-26
• Authors: Joseph Bernstein; Dmitry Gourevitch; Siddhartha Sahi
• Keywords: Hypergeometric distribution

Motivated by the theory of hypergeometric orthogonal polynomials, we consider quasi-orthogonal polynomial families, i.e. those that are with respect to a non-degenerate bilinear form defined linear functional, and in which ratio successive coefficients is given rational function $f(u,s)$ $u$. We call this family Jacobi type. Our main result there precisely five families These classical Jacobi, Laguerre Bessel two more one parameter $E_n^{(c)},F_n^{(c)}$. The last can be expressed through Lommel they positive measure on $\mathbb{R}$ for $c>0$ $c>-1$ respectively. Each obtained as suitable specialization some series.