Semiclassical multiple orthogonal polynomials and the properties of Jacobi-Bessel polynomials

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(alpha 0)(x - a)(alpha 1) e(7/x) (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. (C) 1997 Academic Press.