2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99952We construct a family of BC_n-symmetric biorthogonal abelian functions generalizing Koornwinder's orthogonal polynomials, and prove a number of their properties, most notably analogues of Macdonald's conjectures. The construction is based on a direct construction for a special case generalizing Okounkov's interpolation polynomials. We show that these interpolation functions satisfy a collection of generalized hypergeometric identities, including new multivariate elliptic analogues of Jackson's summation and Bailey's transformation.59 pages, LaTeX (with AMS macros). v2: Minor revisions per referee commentsCombinatoricsQuantum Algebratext