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How can I evaluate this definite integral

$$ \int_0^\infty \frac{\operatorname{Ai}^2(z+a_n)}{z^2}dz $$ where $a_n$ are the zeroes of the Airy function.

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Do you have any reason to think there are closed-form expressions for these? – Robert Israel Dec 23 '12 at 4:04
Yes I think so, – mohamed benbitour Dec 23 '12 at 11:59

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