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  "body": "\n## Summary\n\nThe Stokes phenomenon is the fact that one analytic function can have different asymptotic expansions in different sectors of the complex plane.\nIt occurs for solutions of linear differential equations at an [[irregular singular point|AT1W4MMTYR]].\nAcross certain rays, the Stokes lines, an exponentially small contribution in the expansion switches on or off.\nThe constants that measure the jump are the Stokes multipliers.\nTogether with the formal invariants, the Stokes data classify such equations up to meromorphic equivalence.\nSee the [[definition|H5V4099GN7]].\n\n## Explanations\n\n### L1 human\n\nApproximate formulas for a function near infinity often hold only in some directions.\nFor the Airy function, one simple formula holds when $x$ is large and positive, where the function decays like an exponential.\nFor $x$ large and negative, the function oscillates, and the right formula is a sum of two exponentials, which together make a sine wave.\nThe function is the same everywhere, but its approximation changes form as one turns around the origin.\nStokes discovered this while computing the Airy integral in optics.\n",
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