Geodesic
Zeros and asymptotics of polynomials satisfying three-term recurrence relations with complex coefficients
Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 309-333

Voir la notice de l'article provenant de la source Math-Net.Ru

Under very general conditions on the complex coefficients of a three-term recurrence relation, it is proved that 'almost all' zeros of the polynomials generated by these relations 'accumulate' on a certain segment in the complex plane. From this result follow the convergence of diagonal Padé approximants and a generalization of Van Vleck's theorem on the convergence of $S$-fractions. Another interesting application is an extension of the so-called Nevai–Blumenthal class of polynomials $M(a,2b)$ to the case when $a,b\in{\mathbb C}$. 
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     author = {D. Barrios and G. L. Lopes and E. Torrano},
     title = {Zeros and asymptotics of polynomials satisfying three-term recurrence relations with complex coefficients},
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D. Barrios; G. L. Lopes; E. Torrano. Zeros and asymptotics of polynomials satisfying three-term recurrence relations with complex coefficients. Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 309-333. http://geodesic.mathdoc.fr/item/SM_1995_80_2_a3/