Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions

Starting from the hyperoctahedral multivariate hypergeometric function of Heckman and Opdam (associated with the $B{C}_n$ root system), we arrive – via partial confluent limits in the sense of Oshima and Shimeno – at solutions of the eigenvalue equations for the Toda chain with one-sided boundary perturbations of Pöschl-Teller type and for the hyperbolic Calogero-Sutherland system in a Morse potential. With the aid of corresponding degenerations of the (bispectral dual) difference equations for the Heckman-Opdam hyperoctahedral hypergeometric function, it is deduced that the eigensolutions in question are holomorphic in the spectral variable.