R. Szwarc

most citedBounds on Tur{á}n determinants

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math.CA2007★ 1 cited

Bounds on Tur{á}n determinants

Christian Berg, Ryszard Szwarc

Let μdenote a symmetric probability measure on [-1,1] and let (p_n) be the corresponding orthogonal polynomials normalized such that p_n(1)=1. We prove that the normalized Tur{á}n…

math.CA2007

Positivity of Turán determinants for orthogonal polynomials

Ryszard Szwarc

The orthogonal polynomials $p_{n}$ satisfy Turán's inequality if $p_{n}^{2} (x) - p_{n - 1} (x) p_{n + 1} (x) \geq 0$ for $n \geq 1$ and for all $x$ in the interval of orthogonality. We give general c…