Slowly varying function

A "slowly varying function" is a concept from asymptotic analysis and number theory that refers to a function that grows very slowly compared to a linear function as its argument tends to infinity. More formally, a function \( L(x) \) is said to be slowly varying at infinity if: \[ \lim_{x \to \infty} \frac{L(tx)}{L(x)} = 1 \] for all \( t > 0 \).