In this paper, we show that the kernel function of Cauchy type for type BC intertwines the commuting family of van Diejen's q-difference operators. This result gives rise to a transformation formula for certain multiple basic hypergeometric series of type BC. We also construct a new infinite family of commuting q-difference operators for which the Koornwinder polynomials are joint eigenfunctions. *

New duality transformation formulas are proposed for multiple elliptic hypergeometric series of type BC and of type C. Various transformation and summation formulas are derived as special cases to recover some previously known results.

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