An integral equation \[ (1)\quad (\pi i)^{- 2}\int^{b}_{a}C(t,\tau)| \tau -t|^{\alpha -1}_ 2F_ 1(\beta,\gamma,\alpha,(\tau -t)/(\tau -a))\phi (\tau)d\tau =f(t),\quad a<t<b, \] with the Gaussian hypergeometric function \({}_ 2F_ 1\) is considered in the Hölder space \(H_ 0^{\lambda}([a,b],\rho)\) with an exponential weight \(\rho (t)=(t-a)^{\alpha_ 1}(b-t)^{\alpha_ n}\prod^{n-1}_{j=2}| t-t_ j|^{\alpha_ j}.\)
Solvability criteria for equation (1) with \(\beta =0\) (and, therefore, \({}_ 2F_ 1\equiv 1)\) in weighted Hölder spaces were obtained earlier by B. Rubin. Criteria to be a Fredholm operator and an index formula for equation (1) are announced.