23 citations · 139 across the 14 of their papers we have counts for
14 papers
Orthogonal polynomials, Toda lattices and Painlevé equations
Walter Van Assche
We give a survey of the connection between orthogonal polynomials, Toda lattices and related lattices, and Painlevé equations (discrete and continuous).
Zero distribution of orthogonal polynomials on a -lattice
Walter Van Assche, Quinten Van Baelen
We give the asymptotic behavior of the zeros of orthogonal polynomials, after appropriate scaling, for which the orthogonality measure is supported on the -lattice $\{q^k, k=0,1…
Orthogonal and multiple orthogonal polynomials, random matrices, and Painlevé equations
Walter Van Assche
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful application…
Solution of an Open Problem about Two Families of Orthogonal Polynomials
Walter Van Assche
An open problem about two new families of orthogonal polynomials was posed by Alhaidari. Here we will identify one of them as Wilson polynomials. The other family seems to be new b…
Threefold symmetric Hahn-classical multiple orthogonal polynomials
Ana F. Loureiro, Walter Van Assche
We characterize all the multiple orthogonal threefold symmetric polynomial sequences whose sequence of derivatives is also multiple orthogonal. Such a property is commonly called t…
Multiple Hermite polynomials and simultaneous Gaussian quadrature
Walter Van Assche, Anton Vuerinckx
Multiple Hermite polynomials are an extension of the classical Hermite polynomials for which orthogonality conditions are imposed with respect to normal (Gaussian) weights $w…