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Zeros of Stieltjes and Van Vleck Polynomials
Transactions of the American Mathematical Society
Vol. 252 (Aug., 1979), pp. 197-204
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1998084
Page Count: 8
You can always find the topics here!Topics: Polynomials, Differential equations, Mathematical theorems, Ellipses, Degrees of polynomials, Mathematical functions, Zero, Hypergeometric functions, Mathematical constants
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The study of the polynomial solutions of the generalized Lamé differential equation gives rise to Stieltjes and Van Vleck polynomials. Marden has, under quite general conditions, established varied generalizations of the results proved earlier by Stieltjes, Van Vleck, Bôcher, Klein, and Pólya, concerning the location of the zeros of such polynomials. We study the corresponding problem for yet another form of the generalized Lamé differential equation and generalize some recent results due to Zaheer and to Alam. Furthermore, applications of our results to the standard form of this differential equation immediately furnish the corresponding theorems of Marden. Consequently, our maintheorem of this paper may be considered as the most general result obtained thusfar in this direction.
Transactions of the American Mathematical Society © 1979 American Mathematical Society