On a class of polynomials defined by two orthogonality relations

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.
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