On the asymptotics of the ratio of orthogonal polynomials. II

Let $\mu$ be a positive measure on the circumference $\Gamma=\{z:|z|=1\}$ and let $\mu'=\dfrac{d\mu}{d\theta}>0$ almost everywhere on $\Gamma$. Let $\Phi_n(z)=z^n+\cdots$ be the orthogonal polynomials corresponding to $\mu$, and let $a_n=-\overline{\Phi_{n+1}(0)}$ be their parameters. Then $\lim\limits_{n\to\infty}a_n=0$.
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