Multiple orthogonal polynomials (MOPs) extend the classical notion of orthogonality by satisfying simultaneous orthogonality conditions with respect to several weight functions or measures. This ...

In this paper we extend to the discrete case a Karhunen-Loève expansion already known for continuous families of classical orthogonal polynomials. This expansion involves Krawtchouk polynomials. It ...

Let μ be a positive measure on the real line, with associated orthogonal polynomials { $p_{n}$ }. Let Ima ≠ 0. Then there is an explicit constant $c_{n}$ such that ...

We discuss the application of orthogonal polynomials to the estimation of probability density functions, particularly with regard to accessing features of a portfolio's profit/loss distribution. Such ...