What is "asymptotic formula"

In mathematics, an asymptotic formula for a quantity (function or expression) depending on natural numbers, or on a variable taking real numbers as values, is a function of natural numbers, or of a real variable, whose values are nearly equal to the values of the former when both are evaluated for the same large values of the variable. An asymptotic formula for a quantity is a function which is asymptotically equivalent to the former.

More generally, an asymptotic formula is "a statement of equality between two functions which is not a true equality but which means the ratio of the two functions approaches 1 as the variable approaches some value, usually infinity".