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## Main Question or Discussion Point

Hello,

Is there some way to express the following integral in terms of some simpler functions?

[itex]f(x,s) = \int^{\infty}_{-\infty} dk\, e^{-ks} \text{Ai}(-k) \text{Ai}(x-k) [/itex]

where the parameter [itex]s \in (0,1) [/itex] and the coordinate [itex]x \in (-\infty,+\infty) [/itex]

The best I can come up with is to integrate numerically, but it takes time to get a good resolution :(

Is there some way to express the following integral in terms of some simpler functions?

[itex]f(x,s) = \int^{\infty}_{-\infty} dk\, e^{-ks} \text{Ai}(-k) \text{Ai}(x-k) [/itex]

where the parameter [itex]s \in (0,1) [/itex] and the coordinate [itex]x \in (-\infty,+\infty) [/itex]

The best I can come up with is to integrate numerically, but it takes time to get a good resolution :(