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

In this paper, we show how to construct exceptional orthogonal polynomials (XOP) using isospectral deformations of classical orthogonal polynomials. The construction is based on confluent Darboux

References

SHOWING 1-10 OF 61 REFERENCES

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

A Bochner type characterization theorem for exceptional orthogonal polynomials

Hypergeometric Orthogonal Polynomials and Their q-Analogues

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

Exceptional Laguerre Polynomials

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

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

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

Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials

We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of
...