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Explicit Bounds for Hermite Polynomials in the Oscillatory Region

Published online by Cambridge University Press:  01 February 2010

William H. Foster  and
Ilia Krasikov
William H. Foster
Affiliation:
Department of Mathematical Sciences, Brunel University, Kingston Lane, Uxbridge UB8 3PH, London, william.foster@brunel.ac.uk
Ilia Krasikov
Affiliation:
Department of Mathematical Sciences, Brunel University, Kingston Lane, Uxbridge UB8 3PH, London, mastiik@brunel.ac.uk

Abstract

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We apply a method of positive quadratic forms based on polynomial inequalities to establish sharp explicit bounds on the envelope of Hermite polynomials in the oscillatory region |x| < (2k – 3/2)1/2.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 3 , 2000 , pp. 307 - 314
Copyright
Copyright © London Mathematical Society 2000

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