# Airy function

Calculator and formulas for calculating the Airy functions for complex numbers

## Airy function calculator

This function calculates the Airy functions Ai(x) and Bi(x) for complex numbers.

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

To perform the calculation, enter the complex number, then click the 'Calculate' button.

The Airy function for real numbers and function curves can be found here

Airy function calculator

 Input Real Imaginary Argument + i Decimal places 0 1 2 3 4 6 8 10 Results Ai(x) Bi(x)

## Formulas for Airy Functions

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

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