Asymptotic formulas for ultraspherical polynomials $P\sb n\sp \lambda(x)$ and their zeros for large values of $\lambda$
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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1. It will be recalled that the ultraspherical polynomials are those which are orthogonal on the interval ( — 1, 1), corresponding to the weight function (1— x2)x~1/2, X>—1/2. In what follows X = 0 will also be excluded. The coefficients of these polynomials are functions of the parameter X appearing in the weight function, and the symbol P„(x, X), indicative of this fact, will be used to denot...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1992
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1992-1089404-x