Stokes phenomenon

Summary

The Stokes phenomenon is the fact that one analytic function can have different asymptotic expansions in different sectors of the complex plane. It occurs for solutions of linear differential equations at an irregular singular point. Across certain rays, the Stokes lines, an exponentially small contribution in the expansion switches on or off. The constants that measure the jump are the Stokes multipliers. Together with the formal invariants, the Stokes data classify such equations up to meromorphic equivalence. See the definition.