THE EXTENDED JORDANS LEMMA AND THE RELATION BETWEEN LAPLACE TRANSFORMAND FOURIER-TRANSFORM

Jordan's lemma can be used for a wider range than the original one. Th e extended Jordan's lemma can be described as follows. Let f(z) be ana lytic in the upper half of the z plane (Imz greater than or equal to 0 ), with the exception of a finite number of isolated singularities, an d for p>0, [GRAPHICS] then [GRAPHICS] where z=Re-i phi and CR is the o pen semicircle in the upper half of the z plane. With the extended Jor dan's lemma one can find that Laplace transform and Fourier transform are a pair of integral transforms which relate to each other.