Analog of the Hadamard Formula for the First Ellipse of Meromorphy

Suppose that $P_n$ are orthonormal polynomials on the closed interval $[-1,1]$ which are constructed from a weight function satisfying the Szegö condition. In this paper, we obtain the first ellipse of meromorphy of the function $F(z)=\sum_{n=0}^\infty F_nP_n(z)$, i.e., the maximal ellipse with foci at the points $\pm1$ to which the function $F$ can be extended as a meromorphic function having at most one pole.