LAUSR

Abstract 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 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.