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A proof of Freud's conjecture for exponential weights

Authors:

Institution:

1. National Research Institute for Mathematical Sciences, C.S.I.R., P.O. Box 395, 0001, Pretoria, Republic of South Africa
2. Department of Mathematics, Bowling Green State University, 43403, Bowling Green, Ohio, USA
3. Institute for Constructive Mathematics Department of Mathematics, University of South Florida, 33620, Tampa, Florida, USA

Abstract:

LetW (x) be a function nonnegative inR, positive on a set of positive measure, and such that all power moments ofW ²(x) are finite. Let {p _n(W ²;x)} ₀ denote the sequence of orthonormal polynomials with respect to the weightW ²(x), and let {A _n} ₁ and {B _n} ₁ denote the coefficients in the recurrence relation

$xp_n (W^2 ,x) = A_{n + 1} p_{n + 1} (W^2 ,x) + B_n p_n (W^2 ,x) + A_n p_{n - 1} (W^2 ,x).$

Keywords:	AMS classification" target="_blank">AMS classification Primary 41A25 Primary 42C05
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