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  "body": "\n## Summary\n\nThe Meijer G-function $G^{m, n}_{p, q}$ is a very general special function defined by a [[Barnes integral|1PDGBGEHM2]] of a ratio of products of gamma functions.\nAlmost all classical special functions are particular G-functions, including the exponential function, the Bessel functions and every [[generalized hypergeometric function|VDBAW9PN88]] ${}_pF_q$ with $p \\le q + 1$.\nThe class of G-functions is closed under many operations, such as multiplication by powers, differentiation, Laplace and Mellin transforms, and some integrals of products.\nThis makes it a tool for computing definite integrals in a systematic way, which is used in computer algebra systems.\n\n## Explanations\n\n### L1 human\n\nThe idea is to describe a function by its Mellin transform instead of by a series.\nFor the G-function, the Mellin transform is a ratio of products of gamma functions, and the function itself is recovered by a contour integral.\nBy choosing how many gamma factors go on top and on the bottom, one gets the exponential function, the Bessel functions, the hypergeometric functions and much more.\nThe simplest case is $G^{1, 0}_{0, 1}(- ; 0 \\mid z) = e^{-z}$.\n",
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