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Many special functions appear as solutions of differential equations or integrals of elementary functions. Most special functions have relationships with representation theory of Lie groups.

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A convolution integral of airy functions

I do not know how to solve this problem, but I hope this (comment) would be helpful in someway. One can use the Airy function's integral expression $$ Ai(x) = \frac{1}{2\pi i} \int_{\mathcal{C}} e^{ …
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