On Finite Exceptional Orthogonal Polynomial Sequences Composed of Rational Darboux Transforms of Romanovski-Jacobi Polynomials
Year: 2025
Type: article
Abstract: The paper presents the united analysis of the finite exceptional orthogonal polynomial (EOP) sequences composed of rational Darboux transforms of Romanovski-Jacobi polynomials. It is shown that there are four distinguished exceptional differential polynomial systems (X-Jacobi DPSs) of series J1, J2, J3, and W. The first three X-DPSs formed by pseudo-Wronskians of two Jacobi polynomials contain both exceptional orthogonal polynomial systems (X-Jacobi OPSs) on the interval (-1,+1) and the finite EOP sequences on the positive interval (1,Inf). On the contrary, the X-DPS of series W formed by Wronskians of two Jacobi polynomials contains only (infinitely many) finite EOP sequences on the interval (1,Inf). In addition, the paper rigorously examines the three isospectral families of the associated Liouville potentials (rationally extended hyperbolic Pöschl-Teller potentials of types a, b, and a’) exactly quantized by the EOPs in question.
Source: Axioms
Author: Gregory Natanson
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W4408529599