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  "body": "\n## Summary\n\nScorer's functions $\\operatorname{Gi}$ and $\\operatorname{Hi}$ are particular solutions of the inhomogeneous Airy equations $y'' - x y = \\mp\\frac{1}{\\pi}$.\nThey are built from the same integrals as the [[Airy functions|1N5D4PN92W]], split into two pieces.\nTheir sum is the Airy function $\\operatorname{Bi}$.\nThey appear when a turning-point problem has a constant forcing term.\n\n## Explanations\n\n### L1 human\n\nThe Airy function $\\operatorname{Bi}$ is an integral of a sum of two terms, one exponential and one oscillating.\nTaking each term alone gives Scorer's two functions, $\\operatorname{Hi}$ and $\\operatorname{Gi}$.\nEach piece alone no longer solves the Airy equation, but it solves it up to a constant.\nFor example, $\\operatorname{Hi}(0) = \\frac{1}{\\pi} \\int_0^\\infty e^{-t^3/3}\\, dt$, a positive number.\n",
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