# Bounds for Extreme Zeros of Quasi-orthogonal Ultraspherical Polynomials

@article{Driver2016BoundsFE,
title={Bounds for Extreme Zeros of Quasi-orthogonal Ultraspherical Polynomials},
author={Kathy Driver and Martin E. Muldoon},
journal={arXiv: Classical Analysis and ODEs},
year={2016}
}
• Published 30 January 2016
• Mathematics
• arXiv: Classical Analysis and ODEs
We discuss and compare upper and lower bounds obtained by two different methods for the positive zero of the ultraspherical polynomial $C_{n}^{(\lambda)}$ that is greater than $1$ when $-3/2 < \lambda < -1/2.$ Our first approach uses mixed three term recurrence relations and interlacing of zeros while the second approach uses a method going back to Euler and Rayleigh and already applied to Bessel functions and Laguerre and $q$-Laguerre polynomials. We use the bounds obtained by the second… Expand
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