Ramanujan's master theorem

In mathematics, Ramanujan's master theorem (named after mathematician Srinivasa Ramanujan) 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 ${\displaystyle f(x)\!}$ has an expansion of the form

then the Mellin transform of ${\displaystyle f(x)\!}$ is given by

where ${\displaystyle \Gamma (s)\!}$ is the gamma function.

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