Ramanujan's Master Theorem
This article by Tewodros Amdeberhan, Ivan Gonzalez, Marshall Harrison, Victor H. Moll and Armin Straub has been published in The Ramanujan Journal (to appear).
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.
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