18 papers
Exceptional Hahn and Jacobi polynomials with an arbitrary number of continuous parameters
Antonio J. Durán
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…
New examples of Krall-Meixner and Krall-Hahn polynomials, with applications to the construction of exceptional Meixner and Laguerre polynomials
Antonio J. Durán
We construct new examples of Krall discrete orthogonal polynomials, i.e., orthogonal polynomials with respect to a measure which are also eigenfunctions of a higher order differenc…
Bispectral dual Hahn polynomials with an arbitrary number of continuous parameters
Antonio J. Duran
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 dua…
Bispectral Jacobi type polynomials
Antonio J. Durán, Manuel D. de la Iglesia
We study the bispectrality of Jacobi type polynomials, which are eigenfunctions of higher-order differential operators and can be defined by taking suitable linear combinations of…
Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions
Óscar Ciaurri, Antonio J. Durán, Mario Pérez +1
We introduce Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials as generalizations of Bernoulli and Apostol-Euler polynomials, where the role of the derivative is now played by th…
From Krall discrete orthogonal polynomials to Krall polynomials
Antonio J. Durán
We show how to get Krall polynomials from Krall discrete polynomials using a procedure of passing to the limit in some of the parameters of the family. We also show that this proce…