Geodesic
Analog of the Hadamard Formula for the First Ellipse of Meromorphy
Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 552-568

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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.
Keywords: meromorphic function, holomorphic function, ellipse of meromorphy, Szegö condition, rational function.
Mots-clés : pole, Cauchy–Hadamard formula 
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     author = {V. I. Buslaev},
     title = {Analog of the {Hadamard} {Formula} for the {First} {Ellipse} of {Meromorphy}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {552--568},
     publisher = {mathdoc},
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     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a5/}
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V. I. Buslaev. Analog of the Hadamard Formula for the First Ellipse of Meromorphy. Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 552-568. http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a5/