A recursive construction of joint eigenfunctions for the hyperbolic nonrelativistic Calogero-Moser Hamiltonians

We obtain symmetric joint eigenfunctions for the commuting partial differential operators associated to the hyperbolic Calogero-Moser N-particle system. The eigenfunctions are constructed via a recursion scheme, which leads to representations by multidimensional integrals whose integrands are elementary functions. We also tie in these eigenfunctions with the Heckman–Opdam hypergeometric function for the root system AN−1.