Article ID Journal Published Year Pages File Type
4607708 Journal of Approximation Theory 2010 27 Pages PDF
Abstract

We show that the function ((x−dm)(x−dM))1/4xα/2e−x/2Lk(α)(x) is almost equioscillating with the amplitude 2/π provided kk and αα are large enough. Here Lk(α)(x) is the orthonormal Laguerre polynomial of degree kk and dm,dMdm,dM are some approximations for the extreme zeros. As a corollary we obtain a very explicit, uniform in kk and αα, sharp upper bound on the Laguerre polynomials.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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