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## Homework Statement

Int(-infinity to +infinity) exp[i(t^3/3 + at^2 + bt)]dt = 2pi*exp[ia(2a^2/3 - b)]*Ai(b-a^2)

O.Vallee gives this formula in his book, "Airy Functions and Applications to Physics"

but there are no proof of this formula. I tried to prove this formula, but I failed.

Would you give some hints?

## Homework Equations

Int(-infinity to +infinity) exp[i(t^3/3 + at^2 + bt)]dt = 2pi*exp[ia(2a^2/3 - b)]*Ai(b-a^2)