Jacobi–Angelesco Multiple Orthogonal Polynomials on an r-Star

We investigate type I multiple orthogonal polynomials on r intervals that have a common point at the origin and endpoints at the r roots of unity ω j , j = 0 , 1 , … , r - 1 , with ω = exp ( 2 π i / r ) . We use the weight function | x | β ( 1 - x r ) α , with α , β > - 1 , for the multiple orthogonality relations. We give explicit formulas for the type I multiple orthogonal polynomials, the coefficients in the recurrence relation, and the differential equation, and we obtain the asymptotic distribution of the zeros.