Hyperasymptotic evaluation of the Pearcey integral via Hadamard expansions

We describe high-precision computations of the Pearcey integral Pe ( x , y ) for real x and y by means of Hadamard expansions. Numerical results for ( x , y ) situated in different regions of the x , y -plane are given to illustrate the levels of precision that can be achieved. Particular emphasis is given to computation in the neighbourhood of the two cusped curves associated with Pe ( x , y ) across which there is either a coalescence of saddles or a Stokes phenomenon.