Asymptotics of polynomial solutions of a class of generalized Lamé differential equations
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Kent State University. Institute of Computational Mathematics
Heine-Stieltjes polynomialsVan Vleck polynomialsZerosAsymptotics
Martínez-Finkelshtein, A.; Martínez-González, P.; Orive, R. Asymptotics of polynomial solutions of a class of generalized Lamé differential equations. Electronic Transactions on Numerical Analysis (ETNA), 19: 18-28 (2005). [http://hdl.handle.net/10481/32636]
PatrocinadorThe research of A.M.F. and P.M.G. was partially supported by the Ministry of Science and Technology (MCYT) of Spain through the grant BFM2001-3878-C02-02, and by Junta de Andalucía through Grupo de Investigación FQM 0229. A.M.F. acknowledges also the support of the European Research Network on Constructive Complex Approximation (NeCCA), INTAS 03-51-6637, and of NATO Collaborative Linkage Grant “Orthogonal Polynomials: Theory, Applications and Generalizations,” ref. PST.CLG.979738. The research of R.O. was partially supported by grants from Spanish MCYT (Research Project BFM2001-3411) and Gobierno Autónomo de Canarias (Research Project PI2002/136).
In this paper we study the asymptotic behavior of sequences of Heine-Stieltjes and Van Vleck polynomials for a class of generalized Lamé differential equations connected with certain equilibrium problems on the unit circle.