The Ramanujan master theorem and its implications for special functions

K. Górska, D. Babusci, G. Dattoli, G.H.E. Duchamp, K.A. Penson

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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. © 2012 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)11466 - 11471
Number of pages6
JournalApplied Mathematics and Computation
Volume218
Issue number23
DOIs
Publication statusPublished - 1 Aug 2012
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Computational Mathematics

Cite this

Górska, K., Babusci, D., Dattoli, G., Duchamp, G. H. E., & Penson, K. A. (2012). The Ramanujan master theorem and its implications for special functions. Applied Mathematics and Computation, 218(23), 11466 - 11471. https://doi.org/10.1016/j.amc.2012.05.036