Gap Analysis: No Direct Study on Jacobi Polynomials in Two-Mode Squeezed Thermal States with Photon Addition — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
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 Pn(α,β)(x) — orthogonal on [−1,1] with weight (1−x)α(1+x)β. - Gegenbauer: Cn(λ)(x) = (2λ)n/((λ+1/2)n) Pn(λ−1/2,λ−1/2)(x). - Chebyshev: Tn(x) = Pn(−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
Related
- Phi‑Weighted Jacobi Spectra in Photon‑Added Two‑Mode Squeezed Thermal States via E8 Root Projections — E8 Intelligence Research
- p-Kazhdan-Lusztig Polynomials Unify Modular Characters and Tilting Multiplicities — E8 Intelligence Research
- Bi-orderable knot groups force positive real roots in Alexander polynomials — E8 Intelligence Research
- Twisted Torus Knots: Closed-Form Alexander Polynomials and Fibonacci Determinants — E8 Intelligence Research
- Alexander Polynomials for Knots in the 3-Torus — E8 Intelligence Research
BibTeX
@misc{caldin2026analysis,
title = {{Gap Analysis: No Direct Study on Jacobi Polynomials in Two-Mode Squeezed Thermal States with Photon Addition — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23446922},
url = {https://zenodo.org/records/23446922},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gap Analysis: No Direct Study on Jacobi Polynomials in Two-Mode Squeezed Thermal States with Photon Addition — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23446922
UR - https://zenodo.org/records/23446922
AB - 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^(α,β)(x) — orthogonal on [−1,1] with weight (1−x)^α(1+x)^β. - Gegenbauer: C_n^(λ)(x) = (2λ)_n/((λ+1/2)_n) P_n^(λ−1/2,λ−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
ER -