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

The Ramanujan master theorem and its implications for special functions