Reply to the comments of J. C. Dooley on "Analysis of a magnetic sphere using the Fourier transform: a new approach"

Abstract

We would like to make it clear that the Fourier transform of the vertical magnetic effect due to a sphere, V(x), exists but essentially it reduces to the Hankel transform and we mentioned in that sense "it defies". It has been explicitly dealt with by Sneddon (1974: 79?83). Also, Arfken (1970) stated as "The Hankel transform, a Fourier transform for a Bessel function expansion, represents a limiting case of a Fourier-Bessel series. It occurs in potential problems in cylindrical coordinates". In fact, Dooley himself stated in his discussion" ... for a sphere the 1?D Hankel transform can replace the 2?D Fourier transform."