Three-term recurrence relation

Summary

A three-term recurrence relation is a linear recurrence of order two that links three consecutive terms $u_{n+1}$, $u_n$ and $u_{n-1}$. It is the simplest recurrence beyond first order and appears throughout analysis. Orthogonal polynomials satisfy one, and so do the numerators and denominators of continued fractions and many special functions. Its solutions form a two-dimensional space, which leads to the study of minimal and dominant solutions.