Abstract

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 Pöschl-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.