145 citations · 843 across the 63 of their papers we have counts for
58 papers · 1 filter
Asymptotics of the coefficients of polynomials, asymptotic zero distribution and free probability
Walter Van Assche
The asymptotic behavior of the coefficients of a sequence of polynomials is given under the conditions that all the zeros are real and positive and the zeros have an asymptotic zer…
Ratio and limiting zero distribution asymptotics for symmetric multiple orthogonal polynomials
Ana Loureiro, Walter Van Assche
We investigate the ratio asymptotics and the asymptotic zero distribution of a sequence of polynomials that satisfy a recurrence relation of order with all recurrence coeffic…
Unique special solution for discrete Painlevé II
Walter Van Assche
We show that the discrete Painlevé II equation with starting value has a unique solution for which for every . This solution corresponds to the…
Multiple orthogonal polynomials associated with the exponential integral
Walter Van Assche, Thomas Wolfs
We introduce a new family of multiple orthogonal polynomials satisfying orthogonality conditions with respect to two weights on the positive real line, with $w_1(x)=x^α…
Christoffel functions for multiple orthogonal polynomials
Grzegorz Świderski, Walter Van Assche
We study weak asymptotic behaviour of the Christoffel--Darboux kernel on the main diagonal corresponding to multiple orthogonal polynomials. We show that under some hypotheses the…
Multiple Askey-Wilson polynomials and related basic hypergeometric multiple orthogonal polynomials
Jean Paul Nuwacu, Walter Van Assche
We first show how one can obtain Al-Salam--Chihara polynomials, continuous dual -Hahn polynomials, and Askey--Wilson polynomials from the little -Laguerre and the little -…