In this paper, we introduce a set of discrete orthogonal functions known as dual Hahn
polynomials. The Tchebichef and Krawtchouk polynomials are special cases of dual Hahn …

We show that multiple orthogonal polynomials for r measures (μ1,…, μr) satisfy a system of
linear recurrence relations only involving nearest neighbor multi-indices n→±e→ j, where …

Explicit expressions for the Hahn multiple polynomials of type I, in terms of Kampé de Fériet
hypergeometric series, are given. Orthogonal and biorthogonal relations are proven. Then …

This paper investigates stochastic finite matrices and the corresponding finite Markov chains
constructed using recurrence matrices for general families of orthogonal polynomials and …

The recently found hypergeometric multiple orthogonal polynomials on the step-line by Lima
and Loureiro are shown to be random walk polynomials. It is proven that the corresponding …

Hypergeometric expressions for type I Jacobi–Piñeiro orthogonal polynomials with arbitrary
number of weights Page 1 PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY …

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

In this paper, the authors investigate the case of discrete multiple orthogonal polynomials
with two weights on the step line, which satisfy Pearson equations. The discrete multiple …

The Cholesky factorization of the moment matrix is considered for discrete orthogonal
polynomials of hypergeometric type. We derive the Laguerre–Freud equations when the first …

Contiguous hypergeometric relations for semiclassical discrete orthogonal polynomials are
described as Christoffel and Geronimus transformations. Using the Christoffel–Geronimus …