The asymptotic zero distribution of multiple orthogonal polynomials associated with Macdonald functions

L. ZHANG; P. ROMÁN

JOURNAL OF APPROXIMATION THEORY

ACADEMIC PRESS INC ELSEVIER SCIENCE

Año: 2011 vol. 163 p. 143 - 162

0021-9045

We study the asymptotic zero distribution of type II multiple orthogonal polynomials associated with two Macdonald functions (modified Bessel functions of the second kind). On the basis of the four-term recurrence relation, it is shown that, after proper scaling, the sequence of normalized zero counting measures converges weakly to the first component of a vector of two measures which satisfies a vector equilibrium problem with two external fields. We also give the explicit formula for the equilibrium vector in terms of solutions of an algebraic equation.