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  "body": "\n## Summary\n\nA Meijer G-function transform, or G-transform, is an [[integral transform|YCK709QB06]] on $(0, \\infty)$ whose kernel is a [[Meijer G-function|19JNNN5KV7]] of the product $xy$.\nMany classical transforms are special cases, among them the [[Laplace transform|0V49JEZW06]], the [[Stieltjes transform|RG1HFAYD98]] and transforms with Bessel function kernels.\nThe [[Mellin transform|N5PVGRJE1T]] of a G-function is a ratio of products of gamma functions.\nSo the whole family can be studied at once through the Mellin transform.\n\n## Explanations\n\n### L1 human\n\nThe Meijer G-function is one very flexible special function that contains the exponential, the Bessel functions, the hypergeometric functions and many others.\nUsing it as the kernel of a transform gives one formula that covers a whole zoo of transforms.\nFor example, one choice of parameters makes the kernel $e^{-xy}$, and the G-transform becomes the Laplace transform.\nResults proved once for G-transforms, such as inversion and composition rules, then hold for all these transforms.\n",
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