Relativistic Lame functions revisited

A basis for the eigenfunctions of the relativistic elliptic two-particle Calogero-Moser Hamiltonian is known for a dense set in the natural parameter space. We study the question whether an interpolating basis exists, employing an asymptotic power series ansatz. For the hyperbolic specialization we determine all of the coefficients explicitly, which gives rise to formal interpolating eigenfunctions. For the elliptic case we also need a power series ansatz for the eigenvalues. We obtain the first few coefficients explicitly, thus obtaining evidence for the existence of interpolating formal eigenfunctions and eigenvalues.