The intertwined study of orthogonal polynomials and Painlevé equations continues to be a fertile area of research at the confluence of mathematical analysis and theoretical physics. Orthogonal ...

Orthogonal polynomials have long played a pivotal role in quantum mechanics, offering a robust analytic framework to address exactly solvable models. Their applications range from providing explicit ...

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 ...

Series B (Statistical Methodology) of the Journal of the Royal Statistical Society started out simply as the Supplement to the Journal of the Royal Statistical Society in the Society's centenary year ...

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 ...