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

Using Ramanujan’s Master Theorem, we derive two formulas for Hankel transforms of order zero for even functions using the inverse Mellin transform. The validity of these formulas require some special conditions on the functions. A number of illustrative examples are provided. One of them includes the evaluation of a new parametric integral involving the Bessel function J_0(x) .