## Asymptotic zero distribution for a class of multiple orthogonal polynomials

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- by E. Coussement, J. Coussement and W. Van Assche PDF
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**360**(2008), 5571-5588 Request permission

## Abstract:

We establish the asymptotic zero distribution for polynomials generated by a four-term recurrence relation with varying recurrence coefficients having a particular limiting behavior. The proof is based on ratio asymptotics for these polynomials. We can apply this result to three examples of multiple orthogonal polynomials, in particular Jacobi-Piñeiro, Laguerre I and the example associated with modified Bessel functions. We also discuss an application to Toeplitz matrices.## References

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## Additional Information

**E. Coussement**- Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium
**J. Coussement**- Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium
**W. Van Assche**- Affiliation: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium
- MR Author ID: 176825
- ORCID: 0000-0003-3446-6936
- Email: walter@wis.kuleuven.be
- Received by editor(s): June 19, 2006
- Received by editor(s) in revised form: January 31, 2007
- Published electronically: May 20, 2008
- Additional Notes: This work was supported by INTAS project 03-51-6637, by FWO projects G.0455.04 and G.0184.02 and by OT/04/21 of Katholieke Universiteit Leuven

The second author is a postdoctoral researcher at the Katholieke Universiteit Leuven (Belgium) - © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**360**(2008), 5571-5588 - MSC (2000): Primary 33C45, 42C05; Secondary 15A18
- DOI: https://doi.org/10.1090/S0002-9947-08-04535-2
- MathSciNet review: 2415086