Classification of Laguerre–Hahn orthogonal polynomials of class one

G. Filipuk and M. N. Rebocho

Mathematische Nachrichten, 2020, vol. 293, issue 2, 244-262

Abstract: We study orthogonal polynomials related to Stieltjes functions satisfying Riccati type differential equations with polynomial coefficients, AS′=BS2+CS+D, with max{deg(A),deg(B)}≤3,deg(C)≤2. We derive recurrences for the three‐term recurrence relation coefficients of the orthogonal polynomials, including connections with some forms of discrete Painlevé equations.

Date: 2020
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