Asymptotic zero distribution of multiple orthogonal polynomials associated with Macdonald functions
Preprint
Abstract
We study the asymptotic zero distribution of type II multiple orthogonal polynomials associated with two Macdonald functions (modified Bessel functions of the second kind). Based on 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.Keywords
All Related Versions
This publication has 13 references indexed in Scilit:
- Recurrence relations and vector equilibrium problems arising from a model of non-intersecting squared Bessel pathsJournal of Approximation Theory, 2010
- Non-Intersecting Squared Bessel Paths and Multiple Orthogonal Polynomials for Modified Bessel WeightsCommunications in Mathematical Physics, 2008
- Asymptotic zero distribution for a class of multiple orthogonal polynomialsTransactions of the American Mathematical Society, 2008
- An Equilibrium Problem for the Limiting Eigenvalue Distribution of Banded Toeplitz MatricesSIAM Journal on Matrix Analysis and Applications, 2008
- On the limit behavior of recurrence coefficients for multiple orthogonal polynomialsJournal of Approximation Theory, 2006
- Multiple Orthogonal Polynomials Associated with the Modified Bessel Functions of the First KindConstructive Approximation, 2003
- Some properties of multiple orthogonal polynomials associated with Macdonald functionsJournal of Computational and Applied Mathematics, 2001
- Some classical multiple orthogonal polynomialsJournal of Computational and Applied Mathematics, 2001
- Multiple orthogonal polynomials associated with macdonald functionsIntegral Transforms and Special Functions, 2000
- The Asymptotic Zero Distribution of Orthogonal Polynomials with Varying Recurrence CoefficientsJournal of Approximation Theory, 1999