Closed-Form Finite Recurrences for SU(2) 3nj Symbols

This repository contains materials related to the research paper "Closed-Form Finite Recurrences for SU(2) 3nj Symbols" by Arcticoder.

Abstract

Building on the closed-form hypergeometric representation of SU(2) 3nj symbols, this work presents a finite set of algebraic three-term recurrence relations in the spin labels, together with minimal boundary data, which — under the stated assumptions in the paper — can be used to reconstruct SU(2) 3nj recoupling coefficients. The presentation focuses on the algebraic derivation and illustrative examples; readers should treat the results as theoretical developments that may require additional numerical validation in specific computational settings.

Repository Structure

• index.html and index.md: Web presentation of the research paper
• Closed-Form Finite Recurrences for SU(2) 3nj Symbols.tex: Original LaTeX source
• Closed-Form Finite Recurrences for SU(2) 3nj Symbols.pdf: PDF version of the paper

Website

The published version of this work can be viewed at: https://arcticoder.github.io/su2-3nj-recurrences/

Related Work

• Universal Closed-Form Hypergeometric Representation of SU(2) 3nj Symbols

Scope / Validation & Limitations

• Theoretical focus: The material in this repository emphasizes algebraic derivations and illustrative examples. Applications that rely on numerical computation should validate the recurrence-based reconstruction under their chosen numerical precision and parameter regimes.
• Numerical validation: Some recurrence relations may be sensitive to numerical stability when evaluated in floating-point environments for large spin values; include stability checks and, where practicable, compare recurrence outputs against established 6j/9j/3nj libraries or high-precision arithmetic as part of validation.
• Reproducibility: To reproduce results, re-run the code in index.md/index.html using the same parameter sets and environment details; include any random seeds and environment info in reproducibility artifacts under docs/ if publishing numeric comparisons.
• Limitations: The derivations assume the conditions stated in the paper; extending to edge cases or alternate coupling schemes may require additional boundary data or adapted numerical methods.