Pearcey integral

In mathematics, the Pearcey^[1] integral^[2] is defined as^[3]

\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^[4]

In optics, the Pearcey integral can be used to model diffraction effects at a cusp caustic.

A photograph of a cusp caustic produced by illuminating a flat surface with a laser beam through a droplet of water.

Graphs[]

A plot of the absolute value of the Pearcey integral as a function of its two parameters.

^ "Trevor Pearcey [1919-1998]". 13 January 2015.
^ T. Pearcey, The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 37, 311-317, 1946
^ Frank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert, Charles W. Clark, NIST Handbook of Mathematical Functions, p. 777, Cambridge, 2010
^ R.B.Paris, Hadamard Expansions and Hyperasymptotic Evaluation, p. 207, Encyclopedia of Mathematics and its Applications, 141, Cambridge, 2011

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