Ramanujan's Master Theorem and two formulas for zero-order Hankel transform

Abstract: Using Ramanujan's Master Theorem, two formulas are derived which define the Hankel transforms of order zero with even functions by inverse Mellin transforms, provided these functions and their derivatives obey special conditions. Their validity is illustrated by a number of examples. With a help of one of these formulas, one as yet unknown parametric improper integral of the Bessel function J_0(x) is calculated.