Bounds for Extreme Zeros of Quasi–orthogonal Ultraspherical Polynomials
نویسندگان
چکیده
We discuss and compare upper and lower bounds obtained by two different methods for the positive zero of the ultraspherical polynomial C n that is greater than 1 when −3/2 < λ <−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 method to simplify the proof of the known interlacing of the zeros of (1− x2)C n and C n+1 , for −3/2 < λ < −1/2. Mathematics subject classification (2010): 33C45.
منابع مشابه
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