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Higher order turän inequalities

Journal article published in 1998 by Dimitar K. Dimitrov ORCID
This paper is available in a repository.
This paper is available in a repository.

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Abstract

The celebrated Turan inequalities P-n(2)(x) - Pn-1(x)Pn+1(x) greater than or equal to 0, x is an element of [-1, 1], n greater than or equal to 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 gamma(n)(2) - gamma(n-1)gamma(n+1) greater than or equal to 0, n greater than or equal to 1, which hold for the Maclaurin coefficients of the real entire function psi in the Laguerre-Polya class, psi(x) = Sigma(n=0)(infinity) gamma(n)x(n)/n!.