56 citations · 289 across the 35 of their papers we have counts for
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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…
A classification of coverings yielding Heun-to-hypergeometric reductions
Raimundas Vidunas, Galina Filipuk
Pull-back transformations between Heun and Gauss hypergeometric equations give useful expressions of Heun functions in terms of better understood hypergeometric functions. This art…
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…