From the Fourier transforms, Eqs. (15.22) and (15.23), show that the transformation 1 Inx iw-a-y leads...

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From the Fourier transforms, Eqs. (15.22) and (15.23), show that the transformation 1 Inx iw-a-y leads to and- G(a)= - Fix F(x)= F(x)x-dx -| G(a)x da. 2xi Jy-100 These are the Mellin transforms. A similar change of variables is employed in Sec- tion 15.12 to derive the inverse Laplace transform. From the Fourier transforms, Eqs. (15.22) and (15.23), show that the transformation 1 Inx iw-a-y leads to and- G(a)= - Fix F(x)= F(x)x-dx -| G(a)x da. 2xi Jy-100 These are the Mellin transforms. A similar change of variables is employed in Sec- tion 15.12 to derive the inverse Laplace transform.

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The image contains mathematical definitions for a pair of Mellin transform equations Gt int0infty Fx xt1 dx and Fx frac12pi i intciinftyciinfty Gt xt ... View the full answer