Three-term recurrences

This article discusses three-term recurrence formulas, where each function in a family can be expressed as a linear combination of the two previous terms, with coefficients depending on x but not on n. It provides concrete examples from special functions including Bessel functions (first and second kind), modified Bessel functions, Chebyshev polynomials (first and second kind), Hermite polynomials (physicists' convention), and Legendre polynomials. The author notes the prevalence of such recurrences and references deeper mathematical theories like Bochner's theorem, the Nikiforov–Uvarov method, and Infeld-Hull factorization. This content is relevant to mathematics and computer science, particularly for numerical algorithms and symbolic computation.