Calculator and formulas for calculating the Airy functions for complex numbers
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
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\(\displaystyle Ai(x)=\frac{1}{π}\sqrt{\frac{x}{3}}K_{\frac{1}{3}}\left(\frac{2}{3}x^{\frac{3}{2}}\right)\)
\(\displaystyle Bi(x)=\sqrt{\frac{x}{3}} \left( I_{-\frac{1}{3}} \left( \frac{2}{3}x^{\frac{3}{2}} \right) + I_{\frac{1}{3}}\left(\frac{2}{3}x^{\frac{3}{2}}\right)\right) \)
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