Semiclassical Multiple Orthogonal Polynomials and the Properties of Jacobi–Bessel Polynomials Original Research Article

This paper deals with Hermite–Padé 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, wheresis the class of the semiclassical functional. A special case of polynomials, multiple orthogonal with respect to the semiclassical weight functionw(x)=xα0(x−a)α1 eγ/x(a combination of the classical weights of Jacobi and Bessel), is analyzed in order to obtain the strong (Szegő type) asymptotics and the zero distribution.