Stokes Phenomenon

The asymptotic expansion of the Airy Function $\mathop{\rm Ai}\nolimits (z)$ (and other similar functions) has a different form in different sectors of the Complex Plane.

See also Airy Functions

References

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 609-611, 1953.