Meijer G-Function

The Meijer G-function was introduced by the mathematician Cornelis Simon Meijer in 1936 as a very general function designed to include most of the previously known special functions as particular cases. It was not the only such attempt: the generalized hypergeometric function and the MacRobert E-function shared the same goal, but Meijer's G-function was broad enough to include those as special cases as well. It was originally defined through a series, though the now-standard definition, introduced in full generality by Arthur Erdelyi in 1953, uses a line integral in the complex plane. With this modern definition, most established special functions can be expressed in terms of the Meijer G-function, and the set of G-functions is closed under both differentiation and indefinite integration.