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  "body": "\n## Summary\n\nAn asymptotic scale, also called an asymptotic sequence, is a sequence of functions $\\varphi_0, \\varphi_1, \\dots$ near a point $x_0$.\nEach function in it is negligible compared with the one before it.\nIt is the system of reference functions in which [[asymptotic expansions|BJQTEPEZ9G]] are written.\nThe most common scale is the powers $x^{-n}$ as $x \\to \\infty$, but scales with logarithms, fractional powers or exponentials are also needed.\nFixing a scale makes the coefficients of an expansion unique.\n\n## Explanations\n\n### L1 human\n\nAn asymptotic scale is a ladder of functions, each one much smaller than the previous one when $x$ is close to the limit point.\nIt plays the role that the powers $1, x, x^2, \\dots$ play in a Taylor series.\nAn approximation is then described by saying how many steps of the ladder it gets right.\nFor example, $1, \\frac1x, \\frac{1}{x^2}, \\dots$ is a scale as $x \\to \\infty$, because $\\frac{1/x^{n+1}}{1/x^n} = \\frac1x \\to 0$.\n",
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