The Ramanujan master theorem and its implications for special functions

Details The Ramanujan master theorem and its implications for special functions The Ramanujan master theorem and its implications for special functions

2011-04-18

arxiv.org/abs/1104.3406v1

Physics

Mathematical Physics

12 pages

Scientific paper

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.

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