Bounds for Extreme Zeros of Quasi-orthogonal Ultraspherical Polynomials
نویسندگان
چکیده
منابع مشابه
Bounds for Extreme Zeros of Quasi–orthogonal Ultraspherical Polynomials
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 a...
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Let x1 and xk be the least and the largest zeros of the Laguerre or Jacobi polynomial of degree k. We shall establish sharp inequalities of the form x1 < A, xk > B, which are uniform in all the parameters involved. Together with inequalities in the opposite direction, recently obtained by the author, this locates the extreme zeros of classical orthogonal polynomials with the relative precision,...
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ژورنال
عنوان ژورنال: Journal of Classical Analysis
سال: 2016
ISSN: 1848-5987
DOI: 10.7153/jca-09-08