Orthogonal polynomials in weighted Bergman spaces

Let $w$ be a weight on the unit disk $\mathbb{D}$ having the form $$w(z)=\mathrm{\mid }v(z){\mathrm{\mid }}^2\prod _{k=1}^s{\mid \frac{z-a_k}{1-z{\bar{a}}_k}\mid }^{m_k},m_k>-2,\mathrm{\mid }{a}_k\mathrm{\mid }<1,$$ where $v$ is analytic and free of zeros in $\bar{\mathbb{D}}$, and let $(p_n{)}_{n=0}^{\mathrm{\infty }}$ be the sequence of polynomials ($p_n$ of degree $n$) orthonormal over $\mathbb{D}$ 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 $n\to \mathrm{\infty }$ 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 $v(z{)}^{-1}{\prod }_{k=1}^s(1-z{\bar{a}}_k{)}^{-1}$.