Results on multiple orthogonal polynomials will be surveyed. Multiple orthogonal polynomials are intimately related to Hermite–Pad e approximants and often they are also called Hermite–Pad e polynomials. Special attention will be paid to an application of multiple orthogonal polynomials and to analytic theory of two model families of general multiple orthogonal polynomials, referred to as Angel...

In this paper a brief survey of multiple orthogonal polynomials defined using orthogonality conditions spread out over r different measures are given. We consider multiple orthogonal polynomials on the real line, as well as on the unit semicircle in the complex plane. Such polynomials satisfy a linear recurrence relation of order r+1, which is a generalization of the well known three-term recur...

We show how symmetric orthogonal polynomials can be linked to polynomials associated with certain orthogonal L-polynomials. We provide some examples to illustrate the results obtained. Finally as an application, we derive information regarding the orthogonal polynomials associated with the weight function (1 + kx2)(l x2)~1/2, k>0.

In this paper, we present generalization of matching extensions in graphs and we derive combinatorial interpretation of wide classes of orthogonal and q-orthogonal polynomials. Specifically, we assign general weights to complete graphs, cycles and chains or paths defining matching extensions in these graphs. The generalized matching polynomials of these graphs have recurrences defining various ...