Abstract

Potential theory employs the Fourier integral  
I(u,v,z)=r1exp[2πi(ux+uy)]dxdy,
where  
r2=x2+y2+z2
. Bhattacharyya (1966) obtained the value  
I(u,v,z)=exp(2π|z|u2+v2)/u2+v2
with the use of Bessel functions; the same argument has been repeated often in the geophysical literature (see Courant, 1961; Fuller, 1971; Lourenço, 1972; Gunn, 1975; Weil, 1976; Nabighian, 1984). The following alternative, short derivation involves only elementary functions and may, therefore, be of interest.
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