Editing Airy function (section)

==Fourier transform==
Using the definition of the Airy function Ai(''x''), it is straightforward to show that its [[Fourier transform]] is given by
<math display="block">\mathcal{F}(\operatorname{Ai})(k) := \int_{-\infty}^{\infty} \operatorname{Ai}(x)\ e^{- 2\pi i k x}\,dx = e^{\frac{i}{3} (2\pi k)^3}.</math>This can be obtained by taking the Fourier transform of the Airy equation. Let <math display=inline>\hat y = \frac{1}{2\pi i}\int y e^{-ikx}dx</math>. Then, <math>i\hat y' + k^2 \hat y = 0</math>, which then has solutions <math>\hat y = C e^{ik^3/3}.</math> There is only one dimension of solutions because the Fourier transform requires {{mvar|y}} to decay to zero fast enough; {{math|1=Bi}} grows to infinity exponentially fast, so it cannot be obtained via a Fourier transform.