Asymptotic Expansion of the Pearcey Integral Near the Caustic

An asymptotic expansion of the function \[ P(x,y) = ∫_R {exp \{ {i( {{{t^4 } / 4} + {{xt^2 } / 2} + yt} )} \}dt} \] is constructed which remains uniformly valid as x → - ∞ for $(x,y)$ near the caustic 4x³ + 27y² = 0 in the real $xy$-plane. The result remains valid for a range of complex x and y when P is extended to C × C by analytic continuation.