88 citations · 390 across the 36 of their papers we have counts for
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Mixed type multiple orthogonal polynomials associated with the modified Bessel functions and products of two coupled random matrices
Lun Zhang
We consider mixed type multiple orthogonal polynomials associated with a system of weight functions consisting of two vectors. One vector is defined in terms of scaled modified Bes…
Location of Poles for the Hastings-McLeod Solution to the Second Painlevé Equation
Min Huang, Shuai-Xia Xu, Lun Zhang
We show that the well-known Hastings-McLeod solution to the second Painlevé equation is pole-free in the region $\arg x \in [-\fracπ{3},\fracπ{3}]\cup [\frac{2π}{3},\frac{ 4 π}{3}]…
On Certain Wronskians of Multiple Orthogonal Polynomials
Lun Zhang, Galina Filipuk
We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functi…
Multiple orthogonal polynomials associated with an exponential cubic weight
Walter Van Assche, Galina Filipuk, Lun Zhang
We consider multiple orthogonal polynomials associated with the exponential cubic weight e^{-x^3} over two contours in the complex plane. We study the basic properties of these pol…
Ladder operators and differential equations for multiple orthogonal polynomials
Galina Filipuk, Walter Van Assche, Lun Zhang
In this paper, we obtain the ladder operators and associated compatibility conditions for the type I and the type II multiple orthogonal polynomials. These ladder equations extend…
The generalized Krawtchouk polynomials and the fifth Painlevé equation
Lies Boelen, Galina Filipuk, Christophe Smet +2
We study the recurrence coefficients of the orthogonal polynomials with respect to a semi-classical extension of the Krawtchouk weight. We derive a coupled discrete system for thes…