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 dμ is a given positive measure on [−π, π]. 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.

References

{{springer|title=Szegö polynomial|id=s/s130650|first=A.|last= Bultheel|authorlink= Adhemar Bultheel}}
G. Szegő, "Orthogonal polynomials", Colloq. Publ., 33, Amer. Math. Soc. (1967)