Integral Transforms through Mellin-Barnes Integration

We first delineate the wide range of special functions can be written in terms of the superfunctions MeijerG and FoxH. We then explain how these representations can be applied to evaluate large generic families of integral transforms through Mellin-Barnes integration. Finally, we introduce and show results for the computational realization of this work, ResourceFunction["GenericIntegralTransform"] and demonstrate some applications to problems in math and physical science.