 Note how the Mellin transform of the result merely assembles the gamma factors from the Mellin transforms of the two functions in the integrand.Many of the amazing definite integrals listed in tables or produced by computer algebra systems are nothing but special cases of this formula.The convolution formula can be derived by substituting the defining Mellin–Barnes integral for one of the G-functions, reversing the order of integration, and evaluating the inner Mellin-transform integral.