Hermite and Hermite–Fejér interpolation at Pollaczek zeros

In order to approximate functions defined on \((-1,1)\) $(-1,1)$ , which can grow exponentially at \(\pm 1\) $\pm 1$ , we introduce an Hermite and an Hermite–Fejér-type interpolation process based at Pollaczek-type zeros. We prove the convergence of these processes in weighted uniform and \(L^p-\) $L^p-$ norms and provide error estimates which are comparable with the best weighted approximation in suitable function spaces.