Orthogonal polynomials in weighted Bergman spaces

Let $w$ be a weight on the unit disk $D$ having the form $w\left(z\right)=|v\left(z\right){|}^2\prod _{k=1}^s{\left(\frac{z-a_k}{1-z{\overline{a}}_k}\right)}^{m_k},m_k>-2,|a_k|<1,$where $v$ is analytic and free of zeros in $\overline{D}$, and let ${\left(p_n\right)}_{n=0}^{\infty }$ be the sequence of polynomials ($p_n$ of degree $n$) orthonormal over $D$ with respect to $w$. We give an integral representation for $p_n$ from which it is in principle possible to derive its asymptotic behavior as $n\to \infty$ at every point $z$ of the complex plane, the asymptotic analysis of the integral being primarily dependent on the nature of the first singularities encountered by the function $v{\left(z\right)}^{-1}{\prod }_{k=1}^s{(1-z{\overline{a}}_k)}^{-1}$.