2. The Mellin transform is defined by, Mig(2 ) } = 2-g(z)dz. i) Show that the Mellin transform can be obtained from the Fourier trans- form, 1 F{f(x)} V2TT elki f(x)dx, 1-00 by using the change of variables z = e-, or otherwise. ii) Show that the following convolution property holds for the Mellin trans- form, M f( = F(q)G(1 - q) with F(q) = M{f(2)}, and G(q) = Mig(2)}. iii) Show that the following alternate convolution property also holds for Mellin transforms, MJ 's( 9(s)as ) = F(9) G (9)