2020/06/30 by Edwin Langmann, Masatoshi Noumi, Jun’ichi Shiraishi +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Conjecture #Generalization #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Series (stratigraphy) #Trigonometry #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.3842/sigma.2020.105
published as SIGMA 16 (2020), 105, 26 pages
arxiv created 2020/10/21 · openalex publication_date 2020/10/21 · arxiv updated 2020/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For any variable number, a non-stationary Ruijsenaars function was recently introduced as a natural generalization of an explicitly known asymptotically free solution of the trigonometric Ruijsenaars model, and it was conjectured that this non-stationary Ruijsenaars function provides an explicit solution of the elliptic Ruijsenaars model. We present alternative series representations of the non-stationary Ruijsenaars functions, and we prove that these series converge. We also introduce novel difference operators called T which, as we prove in the trigonometric limit and conjecture in the general case, act diagonally on the non-stationary Ruijsenaars functions.