Higher Order Turán Inequalities
نویسنده
چکیده
The celebrated Turán inequalities P 2 n(x) − Pn−1(x)Pn+1(x) ≥ 0, x ∈ [−1, 1], n ≥ 1, where Pn(x) denotes the Legendre polynomial of degree n, are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of the inequalities γ2 n − γn−1γn+1 ≥ 0, n ≥ 1, which hold for the Maclaurin coefficients of the real entire function ψ in the Laguerre-Pólya class, ψ(x) = ∑∞ n=0 γnx n/n!.
منابع مشابه
Higher Order Turán Inequalities for the Riemann Ξ-function
The simplest necessary conditions for an entire function
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