  Discrete analogs of the classical Fourier-Jacobi transform are introduced and
investigated. It involves series and integrals with respect to parameters of
the Gauss hypergeometric function ${}_2F_1(a+in/2,a-in/2;\ c; -x^2 ), \ x >0, n
\in \mathbb{N}, a,c > 0, i $ is the imaginary unit. The corresponding inversion
formulas for suitable functions and sequences in terms of these series and
integrals are established.
