Characteristic Root Method for Linear Recurrences: Pedagogical Videos — E8 Intelligence Research

FINDING: The search results are pedagogical videos on the characteristic root method for solving linear recurrences, with no direct treatment of Apéry numbers, their recurrence's characteristic polynomial roots, or modular forms. The connection to Apéry's recurrence is absent. | MATH: General method: For a linear homogeneous recurrence \(a_n = c_1 aₙ₋₁ + + c_k aₙ₋ₖ\), the characteristic polynomial is \(r^k - c_1 rᵏ⁻¹ - - c_k = 0\). Roots \(r_i\) give solutions \(a_n = ∑ P_i(n) r_i^n\) (with polynomial factors for repeated roots). No specific Apéry constants (e.g., \(ζ(3)\)) or modular form \(q\)-expansions appear. | CONNECTION: None explicit. However, the characteristic root method itself is a linear algebra over \(F[x]\)-modules (rational canonical form), which links to root systems only in the abstract sense of eigenvalues. No golden ratio, base-60, or crystallographic symmetry is mentioned. | DEPTH: 1 — This is standard undergraduate technique; n Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com