Integral Transforms through Mellin-Barnes Integration

Oleg Marichev and Paco Jain

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