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  "body": "\n## Summary\n\nA three-term recurrence relation is a linear recurrence of order two that links three consecutive terms $u_{n+1}$, $u_n$ and $u_{n-1}$.\nIt is the simplest recurrence beyond first order and appears throughout analysis.\n[[Orthogonal polynomials|8TXASARQN1]] satisfy one, and so do the numerators and denominators of [[continued fractions|04P2RJ4WPS]] and many special functions.\nIts solutions form a two-dimensional space, which leads to the study of minimal and dominant solutions.\n\n## Explanations\n\n### L1 human\n\nEach new term is built from the two terms just before it, with coefficients that may change with $n$.\nThe Fibonacci rule $u_{n+1} = u_n + u_{n-1}$ is the simplest example.\nThe Chebyshev polynomials obey $T_{n+1}(x) = 2x\\, T_n(x) - T_{n-1}(x)$, which lets you compute them one after another from $T_0 = 1$ and $T_1 = x$.\n",
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