  We write spectral decomposition of the hypergeometric differential operator
on the contour $Re z=1/2$ (multiplicity of spectrum is 2). As a result, we
obtain an integral transform that differs from the Jacobi (or Olevsky)
transform. We also try to do a step towards vector-valued special functions and
construct a 3F2 orthogonal basis in the space of functions having values in
2-dimensional space. This basis is lying in an analytic continuation of
continuous dual Hahn polynomials with respect to number $n$ of a polynomial.
  In Addendum, we discuss a vector-value analog of the Meixner--Pollachek
orthogonal system and also perturbations of Laguerre, Meixner, and
  Jacobi polynomials.
