We prove the existence of ratio asymptotic for a sequence of multiple orthogonal polynomials which share orthogonality relations with a collection of m finite Borel measures supported on a bounded interval of the real line and constitute a so called Nikishin system of measures. When m = 1 our result reduces to E. A. Rakhmanov's known Theorem on ratio asymptotic for orthogonal polynomials on a segment.

In this paper we investigate general properties of the coefficients in the recurrence relation satisfied by multiple orthogonal polynomials. The results include as particular cases Angelesco and Nikishin systems.

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This paper deals with Hermite Pade polynomials in the case where the multiple orthogonality condition is related to semiclassical functionals. The polynomials, introduced in such a way, are a generalization of classical orthogonal polynomials (Jacobi, Laguerre, Hermite, and Bessel polynomials). They satisfy a Rodrigues type formula and an (s+2)-order differential equation, where s is the class of the semiclassical functional. A special case of polynomials, multiple orthogonal with respect to the semiclassical weight function w(x)=x : 0 (x&a) : 1 e #Âx (a combination of the classical weights of Jacobi and Bessel), is analyzed in order to obtain the strong (Szego type) asymptotics and the zero distribution.1997 Academic Press