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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)$.

References [Enhancements On Off] (What's this?)

  • [1] S. Ahmed, A. Laforgia and M. E. Muldoon, On the spacing of the zeros of some classical orthogonal polynomials, J. London Math. Soc. (to appear). MR 653383 (83d:34051)
  • [2] G. Szegö, Orthogonal polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R.I., 1975.

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Keywords: Zeros of ultraspherical polynomials, Sturm comparison theorem
Article copyright: © Copyright 1981 American Mathematical Society

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