  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.
