145 citations · 843 across the 63 of their papers we have counts for
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Interlacing properties of zeros of multiple orthogonal polynomials
Maciej Haneczok, Walter Van Assche
It is well known that the zeros of orthogonal polynomials interlace. In this paper we study the case of multiple orthogonal polynomials. We recall known results and some recursion…
Recurrence coefficients of generalized Charlier polynomials and the fifth Painlevé equation
Galina Filipuk, Walter Van Assche
We investigate generalizations of the Charlier polynomials on the lattice , on the shifted lattice and on the bi-lattice $\mathbb{N}\cup (\mathbb{N}+1-…
The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation
Galina Filipuk, Walter Van Assche, Lun Zhang
We show that the coefficients of the three-term recurrence relation for orthogonal polynomials with respect to a semi-classical extension of the Laguerre weight satisfy the fourth…
The nearest neighbor recurrence coefficients for multiple orthogonal polynomials
Walter Van Assche
We show that multiple orthogonal polynomials for r measures satisfy a system of linear recurrence relations only involving nearest neighbor multi-indices $\vec{n}\p…
Orthogonal polynomials on a bi-lattice
Christophe Smet, Walter Van Assche
We investigate generalizations of the Charlier and the Meixner polynomials on the lattice N and on the shifted lattice N+1-β. We combine both lattices to obtain the bi-lattice N \c…