The Airy function is a Fredholm determinant. Menon, G. J. Dynam. Differential Equations, 28(3-4):1031–1038, 2016.
The Airy function is a Fredholm determinant [link]Paper  doi  bibtex   
@article{MR3537363,
	Author = {Menon, Govind},
	Date-Added = {2018-03-21 15:34:07 +0000},
	Date-Modified = {2018-03-21 15:34:07 +0000},
	Doi = {10.1007/s10884-015-9458-6},
	Fjournal = {Journal of Dynamics and Differential Equations},
	Issn = {1040-7294},
	Journal = {J. Dynam. Differential Equations},
	Mrclass = {47G10 (33C10)},
	Mrnumber = {3537363},
	Number = {3-4},
	Pages = {1031--1038},
	Title = {The {A}iry function is a {F}redholm determinant},
	Url = {https://doi.org/10.1007/s10884-015-9458-6},
	Volume = {28},
	Year = {2016},
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