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  "body": "\n## Summary\n\nThe multidimensional Mellin transform takes a function on the open orthant $(0, \\infty)^n$ to a function of $n$ complex variables, by integrating against $x_1^{s_1 - 1} \\cdots x_n^{s_n - 1}$.\nIt is the [[Mellin transform|N5PVGRJE1T]] applied in each variable in turn.\nIt turns dilations in each variable into multiplication by powers, and it is used for the asymptotics of multiple integrals and sums.\n\n## Explanations\n\n### L1 human\n\nThe one-variable Mellin transform measures how a function behaves under stretching of its variable.\nIn several variables each variable may be stretched separately, and one complex exponent is attached to each.\nFor example, $e^{-x_1 - x_2}$ has the two-variable Mellin transform $\\Gamma(s_1)\\Gamma(s_2)$, the product of two gamma functions.\nThe logarithmic change of variables $x_j = e^{-t_j}$ turns it into a multidimensional Laplace or Fourier transform.\n",
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