Barut–Girardello Coherent states for the Gegenbauer oscillator

For the Gegenbauer oscillator, which definition is suggested in this paper, for which the Gegenbauer (ultraspherical) polynomials plays the same role as the Hermite polynomials in the case of usual boson oscillator, we define the family of Barut–Girardello coherent states (the eigenstates of the relevant anihilation operator). We show the validity of unity resolution for this states and evaluate their overlaping. We also show that the given results reproduce the analogous results, obtained early, for the cases of Legendre and Chebyshev polynomials. In the later case we also construct the measure which participate in the unity resolution.