Slowly varying function

Summary

A 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 $a > 0$. Such functions grow or decay more slowly than any positive power of $x$, like the logarithm. They appear as correction factors in Karamata's Tauberian theorem, in probability theory and in the study of asymptotic behaviour.