Airy function

Airy function

The Airy function $\operatorname{Ai}(x)$ is a classical special function that naturally describes transitions near simple turning points in differential equations and asymptotic analysis.

Its oscillatory-to-decaying behaviour makes it a standard local model in wave mechanics, optics, semiclassical analysis and special-function asymptotics.

See also: turning point, asymptotic, scaling law. .