  Our main aim in this self-contained article is at the same time to detail the
relationships between the resurgence and the hyperasymptotic theories, and to
demonstrate how these theories can be used for an implicit resurgent function.
For this purpose we consider after Stokes the question of the effective
Borel-resummation of an exact Bohr-Sommerfeld-like implicit resurgent function
whose values on an explicit semi-lattice provide the zeros of the Airy
function. The resurgent structure encountered resembles what one usually gets
in nonlinear problems, so that the method described here is quite general.
