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Zbl 1034.42021
Kasuga, T.; Sakai, R.
Orthonormal polynomials with generalized Freud-type weights.
(English)
[J] J. Approximation Theory 121, No. 1, 13-53 (2003). ISSN 0021-9045

The authors study polynomials, orthonormal with respect to a generalized Freud-type weight $W_{rQ}^2(x)=\vert x\vert ^{2r}\exp(-2Q(x)),$ where $r>-1/2$ and $\exp(-2Q(x))$ is a Freud weight. They prove infinite-finite range inequalities, estimates of Christoffel functions, the largest zeros and spacing of zeros for those orthonormal polynomials. The results extend and improve corresponding results for other classes of weights [see {\it E.Levin} and {\it D. S. Lubinsky}, Orthogonal polynomials for exponential weights'' (2001; Zbl 0997.42011)].
[Alexei Lukashov (Saratov)]
MSC 2000:
*42C05 General theory of orthogonal functions and polynomials
33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: orthogonal polynomials; exponential weights

Citations: Zbl 0997.42011

Cited in: Zbl 1083.42020

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