Basic Properties of Non-Stationary Ruijsenaars Functions

  title={Basic Properties of Non-Stationary Ruijsenaars Functions},
  author={Edwin Langmann and Masatoshi Noumi and Jun'ichi Shiraishi},
  journal={Symmetry Integrability and Geometry-methods and Applications},
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… 
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