  Motivated by the theory of hypergeometric orthogonal polynomials, we consider
quasi-orthogonal polynomial families - those that are orthogonal with respect
to a non-degenerate bilinear form defined by a linear functional - in which the
ratio of successive coefficients is given by a rational function $f(u,s)$ which
is polynomial in $u$. We call this a family of Jacobi type.
  Our main result is that, up to rescaling and renormalization, there are only
five families of Jacobi type. These are the classical families of Jacobi,
Laguerre and Bessel polynomials, and two more one parameter families
$E_n^{(c)},F_n^{(c)}$. Each family arises as a specialization of some
hypergeometric series. The last two families can also be expressed through
Lommel polynomials, and they are orthogonal with respect to a positive measure
on $\mathbb{R}$ for $c>0$ and $c>-1$ respectively.
  We also consider the more general rational families, i.e. quasi-orthogonal
families in which the ratio $f(u,s)$ of successive coefficients is allowed to
be rational in $u$ as well.
