Airy Function Calculator

The Airy functions \(\displaystyle Ai (x) \) and the related function \(\displaystyle Bi(x)\) denote a special function in mathematics for solving the linear differential equation \(\displaystyle y'' -xy=0\).

To calculate, enter the argument, then click on the 'Calculate' button.

The Airy function here expects a real number as an argument. The Airy function for complex numbers can be found in the complex numbers section.

Formulas for the Airy functions

Description of the Airy function

The Airy function is a special mathematical function commonly found in physics and optics. It is named after the British astronomer George Biddell Airy, who used it in his work on optics. There are several variants of the Airy function, of which \(Ai(z)\) and \(Bi(z)\) are the most common.

\(Ai(z)\): The Airy function of the first kind is a solution of the Airy equation or also called Stokes equation. It occurs in optics, quantum mechanics, electromagnetics and radiation transfer.

\(Bi(z)\): The Airy function of the second kind is another solution to the Airy equation. It is linearly independent of \(Ai(z)\) and is also used in various physical contexts.

The Airy functions are closely related to the solution of the Schrödinger equation for a linear potential well. Their properties, zeros and asymptotic behavior are of particular interest.