Classical multiple orthogonal polynomials of Angelesco system

摘要

In this paper, we analyze more carefully the Rodrigues formula of classical multiple orthogonal polynomials of Angelesco system and consider the sequence of them for the diagonal index case, and then find many properties of such a sequence of orthogonal polynomials. More precisely, we consider the diagonal index sequence {P_(n.n(x)}_(n=0)~∞ of classical multiple orthogonal polynomials {P_(n1.n2(x)}_(n1.n2)~∞ of Angelesco system. For such a sequence we give recurrence relations, differential-difference equations, and then we finally find a third order differential equation having {P_(n.n(x)}_(n=0)~∞ as solutions.