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.
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
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