Geodesic
On a~class of polynomials defined by two orthogonality relations
Sbornik. Mathematics, Tome 38 (1981) no. 4, pp. 563-580

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. 
@article{SM_1981_38_4_a7,
     author = {V. A. Kalyagin},
     title = {On a~class of polynomials defined by two orthogonality relations},
     journal = {Sbornik. Mathematics},
     pages = {563--580},
     publisher = {mathdoc},
     volume = {38},
     number = {4},
     year = {1981},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1981_38_4_a7/}
}
TY  - JOUR
AU  - V. A. Kalyagin
TI  - On a~class of polynomials defined by two orthogonality relations
JO  - Sbornik. Mathematics
PY  - 1981
SP  - 563
EP  - 580
VL  - 38
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1981_38_4_a7/
LA  - en
ID  - SM_1981_38_4_a7
ER  - 
%0 Journal Article
%A V. A. Kalyagin
%T On a~class of polynomials defined by two orthogonality relations
%J Sbornik. Mathematics
%D 1981
%P 563-580
%V 38
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1981_38_4_a7/
%G en
%F SM_1981_38_4_a7
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/