A monotonic property for the zeros of ultraspherical polynomials
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- by Andrea Laforgia PDF
- Proc. Amer. Math. Soc. 83 (1981), 757-758 Request permission
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
- S. Ahmed, A. Laforgia, and M. E. Muldoon, On the spacing of the zeros of some classical orthogonal polynomials, J. London Math. Soc. (2) 25 (1982), no. 2, 246–252. MR 653383, DOI 10.1112/jlms/s2-25.2.246 G. Szegö, Orthogonal polynomials, 4th ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R.I., 1975.
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 757-758
- MSC: Primary 33A45; Secondary 34C10
- DOI: https://doi.org/10.1090/S0002-9939-1981-0630050-X
- MathSciNet review: 630050