Bounds on Turán determinants
نویسندگان
چکیده
Let μ denote a symmetric probability measure on [−1, 1] and let (pn) be the corresponding orthogonal polynomials normalized such that pn(1) = 1. We prove that the normalized Turán determinant ∆n(x)/(1−x), where ∆n = pn−pn−1pn+1, is a Turán determinant of order n− 1 for orthogonal polynomials with respect to (1− x2)dμ(x). We use this to prove lower and upper bounds for the normalized Turán determinant in the interval −1 < x < 1. 2000 Mathematics Subject Classification: Primary 33C45; Secondary 26D07
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عنوان ژورنال:
- Journal of Approximation Theory
دوره 161 شماره
صفحات -
تاریخ انتشار 2009