Airy Function

Calculator and formulas for calculating the Airy functions Ai(x) and Bi(x)

Calculate the Airy function


This page contains an online calculator for the Airy function.

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 \(\displaystyle y'' -xy=0\).


Airy function calculator

 Input
Argument
Decimal places
 Result
Ai(x)
Bi(x)

If you move the mouse over the graphic, the values more or less than the specified argument are displayed.


Formulas for the Airy functions


\(\displaystyle Ai(x)=\frac{1}{π}\sqrt{\frac{x}{3}}K_{\frac{1}{3}}\left(\frac{2}{3}x^{\frac{3}{2}}\right)\)


\(\displaystyle Bi(x)=\sqrt{\frac{x}{3}} \left( I_{-\frac{1}{3}} \left( \frac{2}{3}x^{\frac{3}{2}} \right) + I_{\frac{1}{3}}\left(\frac{2}{3}x^{\frac{3}{2}}\right)\right) \)


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