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  "body": "\n## Summary\n\nThe Airy functions $\\operatorname{Ai}$ and $\\operatorname{Bi}$ are two standard independent solutions of the [[Airy equation|PNESAD6R5T]] $y'' = x y$.\n$\\operatorname{Ai}$ decays rapidly as $x \\to +\\infty$, and $\\operatorname{Bi}$ grows; both oscillate as $x \\to -\\infty$.\nThey describe every simple turning point, where a wave changes from oscillating to decaying.\nThis makes them central in optics near caustics, in quantum mechanics near classical turning points, and in uniform asymptotics of other special functions.\n\n## Explanations\n\n### L1 human\n\nThe equation $y'' = x y$ acts like a spring on the left of $0$ and like exponential growth on the right of $0$.\nThe Airy function $\\operatorname{Ai}$ is the solution that wiggles on the left and dies out quickly on the right.\nIts graph looks like a sine wave whose waves get shorter and lower toward the left, then a single hump near $0$, then a fast decay.\nThe bright bands just inside a rainbow follow the square of $\\operatorname{Ai}$.\n",
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