Asymptotic theory

Asymptotic theory is the branch of mathematics which studies properties of asymptotic expansions.

The most known result of this field is the prime number theorem: Let π(x) be the number of prime numbers that are smaller than or equal to x. The limit

$\lim_{x\rightarrow\infty}\frac{\pi(x)\ln(x)}{x}$

exists.

Some results often neglected include the probability distribution of the likelihood ratio statistic and the expected value of the deviance in statistics, results that are used daily by applied statisticians.

This mathematical analysis-related article is a stub. You can help Wikipedia by expanding it.