Meijer G-function

Summary

The Meijer G-function $G^{m, n}_{p, q}$ is a very general special function defined by a Barnes integral of a ratio of products of gamma functions. Almost all classical special functions are particular G-functions, including the exponential function, the Bessel functions and every generalized hypergeometric function ${}_pF_q$ with $p \le q + 1$. The class of G-functions is closed under many operations, such as multiplication by powers, differentiation, Laplace and Mellin transforms, and some integrals of products. This makes it a tool for computing definite integrals in a systematic way, which is used in computer algebra systems.