The Ramanujan Journal

, Volume 29, Issue 1–3, pp 103–120 | Cite as

Ramanujan’s Master Theorem

  • Tewodros Amdeberhan
  • Olivier Espinosa
  • Ivan Gonzalez
  • Marshall Harrison
  • Victor H. Moll
  • Armin Straub
Article

Abstract

S. Ramanujan introduced a technique, known as Ramanujan’s Master Theorem, which provides an explicit expression for the Mellin transform of a function in terms of the analytic continuation of its Taylor coefficients. The history and proof of this result are reviewed, and a variety of applications is presented. Finally, a multi-dimensional extension of Ramanujan’s Master Theorem is discussed.

Keywords

Integrals Analytic continuation Series representation Hypergeometric functions Random walk integrals Method of brackets 

Mathematics Subject Classification

33B15 33C05 33C45 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Tewodros Amdeberhan
    • 1
  • Olivier Espinosa
    • 2
  • Ivan Gonzalez
    • 2
  • Marshall Harrison
    • 3
  • Victor H. Moll
    • 1
  • Armin Straub
    • 1
  1. 1.Department of MathematicsTulane UniversityNew OrleansUSA
  2. 2.Departmento de FisicaUniversidad Santa MariaValparaisoChile
  3. 3.Prestadigital LLCHoustonUSA

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