Dimitrov, Dimitar K. [UNESP]2014-05-272014-05-271998-12-01Proceedings of the American Mathematical Society, v. 126, n. 7, p. 2033-2037, 1998.0002-9939http://hdl.handle.net/11449/65596The celebrated Turân inequalities P 2 n(x)-P n-x(x)P n+1(x) ≥ 0, x ε[-1,1], n ≥ 1, where P n(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 γ 2 n - γ n-1γ n+1 ≥ 0, n ≥ 1, which hold for the Maclaurin coefficients of the real entire function ψ in the Laguerre-Pölya class, ψ(x) = ∑ ∞ n=0 γ nx n / n!. ©1998 American Mathematical Society.2033-2037engEntire functions in the Laguerre-Pölya classRiemann hypothesisTurân determinantsTurân inequalitiesArtigo10.1090/S0002-9939-98-04438-4WOS:000074694200020Acesso aberto2-s2.0-220444352552-s2.0-22044435255.pdf