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Let  W   α , ρ   =  x   α  (1 –  x  2 )  ρ   e  – Q ( x ) , where  α  &gt; –1  2$\begin{array}{} \displaystyle \frac12 \end{array}$    and  Q  is continuous and increasing on [0, 1), with limit ∞ at 1. This paper deals with orthogonal polynomials for the weightsW   α  ,  ρ   2$\begin{array}{} \displaystyle W^2_{\alpha, \rho} \end{array}$    and gives bounds on orthogonal polynomials, zeros, Christoffel functions and Markov inequalities. In addition, estimates of fundamental polynomials of Lagrange interpolation at the zeros of the orthogonal polynomial and restricted range inequalities are obtained.

Orthogonal polynomials for exponential weights x 2 α (1 – x 2 ) 2 ρ e –2 Q ( x ) on [0, 1)