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  "body": "\n## Summary\n\nA slowly varying function is a positive function $L$ on $(0, \\infty)$ such that $L(ax)/L(x) \\to 1$ as $x \\to \\infty$ for every $a \u003e 0$.\nSuch functions grow or decay more slowly than any positive power of $x$, like the logarithm.\nThey appear as correction factors in [[Karamata's Tauberian theorem|DBEGF38V9H]], in probability theory and in the study of asymptotic behaviour.\n\n## Explanations\n\n### L1 human\n\nA slowly varying function hardly notices if you double or triple its argument, once the argument is large.\nThe logarithm is the standard example: $\\log(2x) = \\log x + \\log 2$, and the extra $\\log 2$ is tiny compared with $\\log x$ for large $x$.\nSo $\\log(2x) / \\log x$ gets closer and closer to $1$.\nA power such as $x^2$ is not slowly varying, because doubling $x$ multiplies $x^2$ by $4$.\n",
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