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In this paper classical solutions of the degenerate fifth Painlevé equation are classified,
which include hierarchies of algebraic solutions and solutions expressible in terms of Bessel …

This paper studies the monic semi‐classical Laguerre polynomials based on previous work
by Boelen and Van Assche, Filipuk et al., and Clarkson and Jordaan. Filipuk et al. proved …

A comprehensive framework has been developed to apply the monomiality principle from
mathematical physics to various mathematical concepts from special functions. This paper …

Given a pair of quasi-definite moment functionals {v 0, v 1} we introduce the concept of
coherence of the second kind in terms of an algebraic relation that the corresponding …

In this paper, we study the orthogonal polynomials with respect to a singularly perturbed
Pollaczek–Jacobi type weight By using the ladder operator approach, we establish the …

The Cholesky factorization of the moment matrix is applied to discrete orthogonal
polynomials on the homogeneous lattice. In particular, semiclassical discrete orthogonal …

The Painlevé-IV equation has two families of rational solutions generated, respectively, by
the generalized Hermite polynomials and the generalized Okamoto polynomials. We apply …

We investigate the recurrence coefficients of discrete orthogonal polynomials on the non-
negative integers with hypergeometric weights and show that they satisfy a system of non …

We discuss polynomials orthogonal with respect to a semi-classical generalized higher-
order Freud weight ω (x; t, λ)=| x| 2 λ+ 1 exp⁡(tx 2− x 2 m), x∈ R, with parameters λ>− 1, t∈ …