Abstract
We investigate higher-degree analogues of the Laguerre inequality p ′ 2 −pp″⩾0, of the form ∑ i=0 m a i p ( i) p ( m− i) ⩾0, and establish a few new inequalities of this type for real polynomials with only real roots and also for a class of entire functions. Some applications to orthogonal polynomials are given.
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