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The Pearcey function is the second member of the heirarchy of canonical diffraction catastrophes classified by catastrophe theory. It describes the diffraction pattern decorating a cusped ray caustic when at amplitude and phase of light are taken into account.

The Pearcey function is defined by the integral identity

Pe(x,y)=∫ds exp[i(s^4+ys^2+xs)]

in the xy-plane.