  We study a number of possible extensions of the Ramanujan master theorem,
which is formulated here by using methods of Umbral nature. We discuss the
implications of the procedure for the theory of special functions, like the
derivation of formulae concerning the integrals of products of families of
Bessel functions and the successive derivatives of Bessel type functions. We
stress also that the procedure we propose allows a unified treatment of many
problems appearing in applications, which can formally be reduced to the
evaluation of exponential- or Gaussian-like integrals.
