Joint Eigenfunctions for the Relativistic Calogero–Moser Hamiltonians of Hyperbolic Type. III. Factorized Asymptotics

@article{Hallnas2019JointEF,
  title={Joint Eigenfunctions for the Relativistic Calogero–Moser Hamiltonians of Hyperbolic Type. III. Factorized Asymptotics},
  author={Martin A. Hallnas and Simon Ruijsenaars},
  journal={International Mathematics Research Notices},
  year={2019}
}
In the two preceding parts of this series of papers, we introduced and studied a recursion scheme for constructing joint eigenfunctions $J_N(a_+, a_-,b;x,y)$ of the Hamiltonians arising in the integrable $N$-particle systems of hyperbolic relativistic Calogero–Moser type. We focused on the 1st steps of the scheme in Part I and on the cases $N=2$ and $N=3$ in Part II. In this paper, we determine the dominant asymptotics of a similarity-transformed function $\textrm{E}_N(b;x,y)$ for $y_j-y_{j+1… 
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