Airy function

In mathematics, the main Airy functions Ai(x) and Bi(x) are defined as the two linearly independent solutions to the differential equation

<math>y'' - xy = 0.<math>

They can be written in physics and its applications; related Airy functions Gi(x) and Hi(x) also exist:

<math>\mathrm{Gi}(x) = \frac{1}{\pi} \int_0^\infty \sin\left(\frac{t^3}{3} + xt\right)\, dt<math>

<math>\mathrm{Hi}(x) = \frac{1}{\pi} \int_0^\infty \exp\left(-\frac{t^3}{3} + xt\right)\, dt<math>