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

 

A monotonic property for the zeros of ultraspherical polynomials


Author: Andrea Laforgia
Journal: Proc. Amer. Math. Soc. 83 (1981), 757-758
MSC: Primary 33A45; Secondary 34C10
MathSciNet review: 630050
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Abstract: It is shown that $ \lambda x_{n,k}^{(\lambda )}$ increases as $ \lambda $ increases for $ 0 < \lambda < 1,k = 1,2, \ldots ,\left[ {\tfrac{n}{2}} \right] $, where $ x_{n,k}^{(\lambda )}$ is the $ k{\text{th}}$ positive zero of ultraspherical polynomial $ P_n^{(\lambda )}(x)$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1981-0630050-X
PII: S 0002-9939(1981)0630050-X
Keywords: Zeros of ultraspherical polynomials, Sturm comparison theorem
Article copyright: © Copyright 1981 American Mathematical Society