  Let $w$ be a weight on the unit disk $\mathbb{D}$ having the form
\[w(z)=|v(z)|^2\prod_{k=1}^s\left|\frac{z-a_k}{1-z\overline{a}_k}\right|^{m_k}\,,\quad
m_k>-2,\ |a_k|<1,\] where $v$ is analytic and free of zeros in
$\overline{\mathbb{D}}$, and let $(p_n)_{n=0}^\infty$ 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 $n\to\infty$ 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
$v(z)^{-1}\prod_{k=1}^s(1-z\overline{a}_k)^{-1}$.
