Pearcey integral

In mathematics, the Pearcey integral is defined as


 * $$\operatorname{Pe}(x,y)=\int_{-\infty}^\infty \exp(i(t^4+xt^2+yt)) \, dt.$$

The Pearcey integral is a class of canonical diffraction integrals, often used in wave propagation and optical diffraction problems The first numerical evaluation of this integral was performed by Trevor Pearcey using the quadrature formula. In optics, the Pearcey integral can be used to model diffraction effects at a cusp caustic, which corresponds to the boundary between two regions of geometric optics: on one side, each point is contained in three light rays; on the other side, each point is contained in one light ray.