Near-minimax approximation and telescoping procedures based on Laguerre and Hermite polynomials

Abstract

Suitably chosen systems of generalized Laguerre and Hermite polynomials are shown to provide near-minimax approximations to zero with respect to the weight functions e^−x and x^1/2 e^−x on [o,∞) and the weight function e^−x2 on (−∞,∞). For certain functions which decay exponentially and which may be well approximated by transformed Taylor series, these Laguerre and Hermite polynomials may be exploited in telescoping procedures so as to produce near-minimax approximations of lower degree. Such a procedure is illustrated in the determination of compact and accurate rational approximations to a classical solution on [o,∞) of the Blasius equation.