Corresponding to each (x,y) in the plot of the Pearcey integral is a function of u, f(x,y,u)=∫exp(i(t⁴+xt²+yt))dt where dt is from -∞ to u. f(x,y,.):ℝ->ℂ gives a curve in the complex plane. It's a family of Cornu-like spirals as I drag my mouse around the plot.pic.twitter.com/8McV3aS24q
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Is there a known relationship between the Pearcey integral and the Painleve transcendents?
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I may have asked about that before? http://math-functions-1.watson.jp/sub1_spec_320.html …
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