Turán's inequality for ultraspherical polynomials revisited
نویسندگان
چکیده
منابع مشابه
An extension of Turán’s inequality for ultraspherical polynomials∗
Let pm(x) = P (λ) m (x)/P (λ) m (1) be the m-th ultraspherical polynomial normalized by pm(1) = 1. We prove the inequality |x|pn(x)−pn−1(x)pn+1(x) ≥ 0, x ∈ [−1, 1], for −1/2 < λ ≤ 1/2. Equality holds only for x = ±1 and, if n is even, for x = 0. Further partial results on an extension of this inequality to normalized Jacobi polynomials are given.
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2023
ISSN: ['1331-4343', '1848-9966']
DOI: https://doi.org/10.7153/mia-2023-26-22