Starting from the hyperoctahedral multivariate hypergeometric function of Heckman and Opdam (associated with the BCn root system), we arrive-via partial confluent limits in the sense of Oshima and Shimeno-at solutions of the eigenvalue equations for the quantum Toda chain with one-sided boundary perturbations of Poschl-Teller type and for the hyperbolic quantum 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. (C) 2019 Elsevier Inc. All rights reserved.