Geodesic
Basic Properties of Non-Stationary Ruijsenaars Functions
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\mathcal{T}$ which, as we prove in the trigonometric limit and conjecture in the general case, act diagonally on the non-stationary Ruijsenaars functions.
Keywords: elliptic integrable systems, elliptic hypergeometric functions, Ruijsenaars systems. 
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     author = {Edwin Langmann and Masatoshi Noumi and Junichi Shiraishi},
     title = {Basic {Properties} {of~Non-Stationary} {Ruijsenaars} {Functions}},
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     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a104/}
}
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Edwin Langmann; Masatoshi Noumi; Junichi Shiraishi. Basic Properties of Non-Stationary Ruijsenaars Functions. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a104/

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