Iterated Laguerre and Turán Inequalities

Higher Order Turán Inequalities

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 L...

Turán Inequalities and Zeros of Orthogonal Polynomials∗

We use Turán type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the three term recurrence pk+1 = xpk − ckpk−1, with a nondecreasing sequence {ck}. As a special case they include a non-asymptotic version of Máté, Nevai and Tot...

On Some Turán-type Inequalities

Higher Order Turán Inequalities for the Riemann Ξ-function

The simplest necessary conditions for an entire function

Turán Inequalities and Subtraction-free Expressions

By using subtraction-free expressions, we are able to provide a new proof of the Turán inequalities for the Taylor coefficients of a real entire function when the zeros belong to a specified sector.