Special cases: , fold catastrophe; , cusp catastrophe; , swallowtail catastrophe.
with the contour passing to the lower right of .
with the contour passing to the upper right of .
is related to the Airy function (§9.2):
is the Pearcey integral (Pearcey (1946)):
(Other notations also appear in the literature.)
For the Bessel function see §10.2(ii).
Addendum: For further special cases see §36.2(iv)
(rotation by in plane).
Here the functions and are the complex conjugates of the functions and , respectively.