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  "body": "\n## Summary\n\nA Fuchsian equation is a linear differential equation with rational coefficients whose singular points are all [[regular singular points|H96HXG6CA0]].\nThis includes the point $\\infty$ of the Riemann sphere.\nIts solutions are multivalued functions of controlled growth, described near each singular point by [[Fuchs' theorem|6EZ400WM94]].\nThe equation is largely determined by its singular points, its exponents and its [[monodromy|C8HD62AB6Q]].\nThe hypergeometric equation, the Legendre equation and the Riemann equation are Fuchsian.\nSee the [[definition|YT2B9KQ0BG]].\n\n## Explanations\n\n### L1 human\n\nA Fuchsian equation has finitely many bad points, and at each of them the solutions only behave like powers and logarithms.\nNothing wild happens anywhere, not even at infinity.\nThe Gauss hypergeometric equation is the main example, with bad points $0$, $1$ and $\\infty$.\nThe Bessel equation is not Fuchsian, because its solutions oscillate like $\\sin z$ near $\\infty$.\n",
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