Airy Function - Fourier Transform

Fourier Transform

Using the definition of the Airy function, it is straightforward to show its Fourier transform is given by

\mathcal{F}(\mathrm{Ai})(k) := \int_{-\infty}^{\infty} \mathrm{Ai}(x)\ \mathrm{e}^{- 2\pi \mathrm{i} k x}\,dx = \mathrm{e}^{\frac{\mathrm{i}}{3}(2\pi k)^3}\,.

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