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Laguerre-Angelesco multiple orthogonal polynomials on an r-star

Journal Contribution - Journal Article

We investigate the type I and type II multiple orthogonal polynomials on an r-star with weight function $|x|^{\beta}e^{-x^r}$, with $\beta>-1$. Each measure $\mu_j$, for $1\leq j \leq r$, is supported on the semi-infinite interval $[0,\omega^{j-1}\infty)$ with $\omega=e^{2\pi i/r}$. 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.
Journal: Journal of approximation theory
ISSN: 0021-9045
Volume: 250
Publication year:2020
BOF-keylabel:yes
IOF-keylabel:yes
BOF-publication weight:1
CSS-citation score:1
Authors from:Higher Education
Accessibility:Open