Szegő polynomial

In mathematics, a Szegő polynomial is one of a family of orthogonal polynomials for the Hermitian inner product


 * $$\langle f|g\rangle = \int_{-\pi}^{\pi}f(e^{i\theta})\overline{g(e^{i\theta})}\,d\mu$$

where d&mu; is a given positive measure on [&minus;&pi;, &pi;]. Writing $$\phi_n(z)$$ for the polynomials, they obey a recurrence relation


 * $$\phi_{n+1}(z)=z\phi_n(z) + \rho_{n+1}\phi_n^*(z)$$

where $$\rho_{n+1}$$ is a parameter, called the reflection coefficient or the Szegő parameter.