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- Publisher
- Springer Journals
- Copyright
- Copyright © 2015 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
- ISSN
- 1617-9447
- eISSN
- 2195-3724
- DOI
- 10.1007/s40315-015-0146-7
- Publisher site
- See Article on Publisher Site
Abstract
Motivated by the study of the asymptotic behavior of Jacobi polynomials $$\left( P_{n}^{(nA,nB)}\right) _{n}$$ P n ( n A , n B ) n with $$A\in \mathbb {C}$$ A ∈ C and $$B>0$$ B > 0 , we establish the global structure of trajectories of the related rational quadratic differential on $$\mathbb {C}$$ C . As a consequence, the asymptotic zero distribution $$\left( \text {limit of the root-counting measures of} \left( P_{n}^{(nA,nB)}\right) _{n}\right) $$ limit of the root-counting measures of P n ( n A , n B ) n is described. The support of this measure is formed by an open arc in the complex plane (critical trajectory of the aforementioned quadratic differential) that can be characterized by the symmetry property of its equilibrium measure in a certain external field.
Journal
Computational Methods and Function Theory – Springer Journals
Published: Dec 8, 2015