Geodesic
On a class of polynomials defined by two orthogonality relations
Sbornik. Mathematics, Tome 38 (1981) no. 4, pp. 563-580 
V. A. Kalyagin. On a class of polynomials defined by two orthogonality relations. Sbornik. Mathematics, Tome 38 (1981) no. 4, pp. 563-580. http://geodesic.mathdoc.fr/item/SM_1981_38_4_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper asymptotic representations are obtained for polynomials defined by two orthogonality relations (on the intervals $[-1, 0]$ and $[0, 1]$) with weight $p(x)=(1-x)^\alpha(1+x)^\beta|x|^\gamma$. As in the classical case, the asymptotic expressions are different for $x\in\mathbf C\setminus[-1,1]$ and $x\in[-1,1]$. Asymptotic expressions are also obtained for functions analogous to functions of the second kind, and estimates of the Christoffel coefficients are found. Bibliography: 4 titles.

[1] E. M. Nikishin, “O sisteme markovskikh funktsii”, Vestnik MGU, seriya matem. mekh., 1979, no. 4, 60–63 | MR | Zbl

[2] G. Sege, Ortogonalnye mnogochleny, Fizmatgiz, Moskva, 1962

[3] E. M. Nikishin, “Ob irratsionalnosti znachenii $F(x,s)$”, Matem. sb., 109(151) (1979), 410–417 | MR | Zbl

[4] M. Tsuji, “On a power series which has only algebraic singularities on its convergence circle”, Japan J. Math., 3 (1926), 69–85 | Zbl