Pearcey integral
In mathematics, the Pearcey integral is defined as Pe ( x , y ) = ∫ − ∞ ∞ exp ( i ( t 4 + x t 2 + y t ) ) d t . {\displaystyle \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.