Laguerre–Angelesco multiple orthogonal polynomials on an [formula omitted]-star

Abstract

We investigate the type I and type II multiple orthogonal polynomials on an r-star with weight function |x|βe−xr, with β>−1. Each measure μj, for 1≤j≤r, is supported on the semi-infinite interval [0,ωj−1∞) with ω=e2πi∕r. For both the type I and the type II polynomials we give explicit expressions, the coefficients in the recurrence relation, the differential equation and we obtain the asymptotic zero distribution of the polynomials on the diagonal. Also, we give the connection between the Laguerre–Angelesco polynomials and the Jacobi–Angelesco polynomials on an r-star.