Efficient Formulas for the Maslov Canonical Operator near a Simple Caustic

We revive well-known old formulas for the asymptotics of rapidly oscillating integrals with two nearly coincident saddle points and present an efficient approach to the computation of functions represented by Maslov’s canonical operator near a simple caustic in an algorithmic fashion convenient for implementation on software like Wolfram Mathematica. The exposition is elementary and assumes that no preliminary information about the canonical operator is be known to the reader.