BC-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials

We consider 3-parametric polynomials P*μ(cursive Greek chi; q, t, s) which replace the An-series interpolation Macdonald polynomials P*μ(cursive Greek chi; q, t) for the BCn-type root system. For these polynomials we prove an integral representation, a combinatorial formula, Pieri rules, Cauchy identity, and we also show that they do not satisfy any rational q-difference equation. As s → ∞ the polynomials P*μ(cursive Greek chi; q, t, s) become P*μ(cursive Greek chi; q, t). We also prove a binomial formula for 6-parametric Koornwinder polynomials.