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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Stieltjes and Van Vleck polynomials
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by Neyamat Zaheer PDF
Proc. Amer. Math. Soc. 60 (1976), 169-174 Request permission

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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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 60 (1976), 169-174
  • MSC: Primary 33A70
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0419898-2
  • MathSciNet review: 0419898