Abstract

The Taylor series for the point characteristic V of the refracting plane is investigated. The exact radius of convergence of the series is found. Once the behavior of V near its singularities has been determined, a sequence of increasingly detailed asymptotic relations for the Taylor coefficients υn of V is obtained, n being assumed sufficiently large. A particular, more-or-less arbitrarily chosen, case is studied numerically. The extent to which the values of the υn given by the most detailed of the asymptotic relations agree with their exact values is remarkable, and the “asymptotic region” extends virtually down to n = 2.

© 1986 Optical Society of America

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