Published online by Cambridge University Press: 18 May 2009
The integral function
is known as Airy's Integral since, when z is real, it is equal to the integral
which first arose in Airy's researches on optics. It is readily seen that w= Ai(z) satisfies the differential equation d2w/dz2 = zw, an equation which also has solutions Ai(ωz), Ai(ω2z), where ω is the complex cube root of unity, exp 2/3πi. The three solutions are connected by the relation.