  Consider a root system of type $BC_1$ on the real line $\mathbb R$ with
general positive multiplicities. The Cherednik-Opdam transform defines a
unitary operator from an $L^2$-space on $\mathbb R$ to a $L^2$-space of
$\mathbb C^2$-valued functions on $\mathbb R^+$ with the Harish-Chandra measure
$|c(\lam)|^{-2}d\lam$.
  By introducing a weight function of the form $\cosh^{-\sig}(t)\tanh^{2k} t$
on $\mathbb R$ we find an orthogonal basis for the $L^2$-space on $\mathbb R$
consisting of even and odd functions expressed in terms of the Jacobi
polynomials (for each fixed $\sig$ and $k$). We find a Rodrigues type formula
for the functions in terms of the Cherednik operator. We compute explicitly
their Cherednik-Opdam transforms. We discover thus a new family of $\mathbb
C^2$-valued orthogonal polynomials. In the special case when $k=0$ the even
polynomials become Wilson polynomials, and the corresponding result was proved
earlier by Koornwinder.
