InverseMellinTransform

InverseMellinTransform[expr, s, x] gives the inverse Mellin transform of expr.

Examples

Inverse Mellin transform of Gamma:

InverseMellinTransform[Gamma[s], s, x]
(* Exp[-x] *)

Round-trip verification:

f = Exp[-x];
InverseMellinTransform[MellinTransform[f, x, s], s, x]

Transform of a product:

InverseMellinTransform[Gamma[s] Gamma[1 - s], s, x]

Please visit the official Wolfram Language Reference for more details.