# Exceptional Hahn and Jacobi polynomials with an arbitrary number of continuous parameters

@article{Duran2021ExceptionalHA, title={Exceptional Hahn and Jacobi polynomials with an arbitrary number of continuous parameters}, author={Antonio J. Dur'an}, journal={Studies in Applied Mathematics}, year={2021}, volume={148}, pages={606 - 650} }

We construct new examples of exceptional Hahn and Jacobi polynomials. Exceptional polynomials are orthogonal polynomials with respect to a measure which are also eigenfunctions of a second‐order difference or differential operator. In mathematical physics, they allow the explicit computation of bound states of rational extensions of classical quantum‐mechanical potentials. The most apparent difference between classical or classical discrete orthogonal polynomials and their exceptional…

## 2 Citations

Exceptional Gegenbauer polynomials via isospectral deformation

- MathematicsStudies in Applied Mathematics
- 2022

We show a method to construct isospectral deformations of classical orthogonal polynomials. The construction is based on confluent Darboux transformations, and it allows to construct Sturm-Liouville…

Bispectral dual Hahn polynomials with an arbitrary number of continuous parameters

- Mathematics
- 2021

We construct new examples of bispectral dual Hahn polynomials, i.e., orthogonal polynomials with respect to certain superposition of Christoffel and Geronimus transforms of the dual Hahn measure and…

## References

SHOWING 1-10 OF 77 REFERENCES

Invariance properties of Wronskian type determinants of classical and classical discrete orthogonal polynomials

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

A Bochner type characterization theorem for exceptional orthogonal polynomials

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

Hypergeometric Orthogonal Polynomials and Their q-Analogues

- Mathematics
- 2010

Definitions and Miscellaneous Formulas.- Classical orthogonal polynomials.- Orthogonal Polynomial Solutions of Differential Equations.- Orthogonal Polynomial Solutions of Real Difference Equations.-…

Exceptional Laguerre Polynomials

- Mathematics, Philosophy
- 2018

The aim of this paper is to present the construction of exceptional Laguerre polynomials in a systematic way and to provide new asymptotic results on the location of the zeros. To describe the…

Rational extensions of the trigonometric Darboux-Pöschl-Teller potential based on para-Jacobi polynomials

- Mathematics
- 2014

The possibility for the Jacobi equation to admit, in some cases, general solutions that are polynomials has been recently highlighted by Calogero and Yi, who termed them para-Jacobi polynomials. Such…

Disconjugacy, regularity of multi-indexed rationally extended potentials, and Laguerre exceptional polynomials

- Mathematics
- 2012

The power of the disconjugacy properties of second-order differential equations of Schrodinger type to check the regularity of rationally extended quantum potentials connected with exceptional…

Exactly solvable quantum mechanics and infinite families of multi-indexed orthogonal polynomials

- Mathematics
- 2011

Exceptional Charlier and Hermite polynomials

- J Approx Theory
- 2014

Exceptional Hahn and Jacobi orthogonal polynomials

- MathematicsJ. Approx. Theory
- 2017