Ramanujan's master theorem
Mathematical theorem / From Wikipedia, the free encyclopedia
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In mathematics, Ramanujan's Master Theorem, named after Srinivasa Ramanujan,[1] is a technique that provides an analytic expression for the Mellin transform of an analytic function.
The result is stated as follows:
If a complex-valued function has an expansion of the form
then the Mellin transform of is given by
where is the gamma function.
It was widely used by Ramanujan to calculate definite integrals and infinite series.
Higher-dimensional versions of this theorem also appear in quantum physics (through Feynman diagrams).[2]