The Ramanujan master theorem and its implications for special functions

Abstract

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.

12 pages

References in corpus (1)

• Laguerre-type derivatives: Dobinski relations and combinatorial identities

Cited by in corpus (6)

• Umbral Calculus, a Different Mathematical Language
• Symbolic methods for the evaluation of sum rules of Bessel functions
• Operational Methods in the Study of Sobolev-Jacobi Polynomials
• An Operational Calculus Generalization of Ramanujan's Master Theorem
• On the logarithm of the derivative operator
• The Humbert-Bessel functions, Stirling numbers and probability distributions in coincidence problems