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Starting from the hyperoctahedral multivariate hypergeometric function ofHeckman and Opdam (associated with the $BC_n$ root system), we arrive -- viapartial confluent limits in the sense of Oshima and Shimeno -- at solutions ofthe eigenvalue equations for the Toda chain with one-sided boundaryperturbations of P\"oschl-Teller type and for the hyperbolicCalogero-Sutherland system in a Morse potential. With the aid of correspondingdegenerations of the (bispectral dual) difference equations for theHeckman-Opdam hyperoctahedral hypergeometric function, it is deduced that theeigensolutions in question are holomorphic in the spectral variable.

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