Asymptoticaly expansible solutions for the Helmholtz equation

Abstract

Much attention has been paid in recent years to expansions in the form, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u = e^{ikL} \Sum' \min{\nu} \frac{A_{\nu}}{(ik)^{\nu}}</tex> (1) By means of these expansions many problems of diffraction have been investigated. Though in many particular cases, it has been found that the series of this form are the asymptotic ones, our present knowledge concerning the whole family of solutions admitting asymptotic expansions is still unsatisfactory. From among recent works on this subject the author will mention a very interesting one concerning expansions of a similar type.