On a system of ``classical'' polynomials of simultaneous orthogonality (Q1919424)

Let \(Q_{\overline n}(x)\), \(\overline n=(n_1,n_2)\), be the system of polynomials of simultaneous orthogonality [see \textit{E. M. Nikishin} and \textit{V. N. Sorokin}: ``Rational approximations and orthogonality'' (Russian orig. 1988; Zbl 0718.41002; Engl. transl. 1991; Zbl 0733.41001)] with \(\Delta_1=[a;0]\), \(\Delta_2=[0;1] (-1\leq a<0)\) and \(d\mu_i=|h(x)|dx\), \(h(x)=(x-a)^\alpha(x-1)^\beta x^\gamma\) \((\alpha,\beta,\gamma>-1)\). The differential equation of third-order, the limit periodic behaviour of recurrence coefficients, and the ratio asymptotics for those polynomials are obtained.