The asymptotic series of the Airy function 
(and other similar functions) has a different form in different sectors of the complex plane.
Stokes Phenomenon
See also
Airy FunctionsExplore with Wolfram|Alpha
References
Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 609-611, 1953.Referenced on Wolfram|Alpha
Stokes PhenomenonCite this as:
Weisstein, Eric W. "Stokes Phenomenon." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StokesPhenomenon.html