# Derivative Airy function

Calculator for the derived Airy functions for complex numbers

## Calculate derivative Airy functions

This function calculates the derivative Airy function for complex numbers.

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

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 functions calculator

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

## Formulas for the derivative Airy Functions

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

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