Gap Analysis: No Direct Study on Jacobi Polynomials in Two-Mode Squeezed Thermal States with Photon Addition — E8 Intelligence Research

FINDING: The search results are a scattered mix — no direct paper on "Jacobi polynomials in two-mode squeezed thermal states with photon addition" was retrieved. The closest mathematical anchors are: (a) a 2025 GPU elastodynamics paper using Jacobi/Gauss-Seidel (JGS2), (b) a lecture on Jacobi/Gegenbauer/Chebyshev polynomials, (c) an MIT lecture on two-photon excitation, (d) a Wolfram demo on Jacobi collocation, (e) a dual-rail photon quantum computation lecture, and (f) a hexaquark decay paper. No unified quantum-optical result emerges. MATH: - Jacobi polynomials \(P_n^{(\alpha,\beta)}(x)\) — orthogonal on \([-1,1]\) with weight \((1-x)^\alpha(1+x)^\beta\). - Gegenbauer: \(C_n^{(\lambda)}(x) = \frac{(2\lambda)_n}{(\lambda+1/2)_n} P_n^{(\lambda-1/2,\lambda-1/2)}(x)\). - Chebyshev: \(T_n(x) = P_n^{(-1/2,-1/2)}(x)\) (scaled). - JGS2: iterative solver — no closed-form constants given. - Hexaquark: SU(3) antidecuplet — group theory, no explicit ratios in abstract. - No occurren

Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com