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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Stieltjes and Van Vleck polynomials


Author: Neyamat Zaheer
Journal: Proc. Amer. Math. Soc. 60 (1976), 169-174
MSC: Primary 33A70
MathSciNet review: 0419898
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Abstract: Stieltjes and Van Vleck polynomials arise in the study of the polynomial solutions of the generalized Lamé differential equation. The problem of determining the location of the zeros of such polynomials has been studied under quite general conditions by Marden. He has obtained (see Trans. Amer. Math. Soc. 33 (1931), 934-944) varied generalizations of certain results proved earlier by Stieltjes, Van Vleck, Bôcher, Klein, and Pólya. Our object in this paper is to study certain aspects of the corresponding problem in relation to yet another form of the generalized Lamé differential equation. Furthermore, applications of our theorems to the standard form of the generalized Lamé differential equation immediately furnish the corresponding results due to Stieltjes, Van Vleck, and Marden (cf. the paper cited above).


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DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0419898-2
PII: S 0002-9939(1976)0419898-2
Keywords: Generalized Lamé differential equations, Stieltjes polynomials, Van Vleck polynomials
Article copyright: © Copyright 1976 American Mathematical Society