Monotonicity Properties of the Zeros of Ultraspherical Polynomials
نویسندگان
چکیده
منابع مشابه
Monotonicity of zeros of Jacobi polynomials
Denote by xn,k(α, β), k = 1, . . . , n, the zeros of the Jacobi polynomial P (α,β) n (x). It is well known that xn,k(α, β) are increasing functions of β and decreasing functions of α. In this paper we investigate the question of how fast the functions 1 − xn,k(α, β) decrease as β increases. We prove that the products tn,k(α, β) := fn(α, β) (1− xn,k(α, β)), where fn(α, β) = 2n2 + 2n(α + β + 1) +...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1999
ISSN: 0021-9045
DOI: 10.1006/jath.1996.3259