Orthogonal polynomials on the unit circle

In mathematics, orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle in the complex plane, for some probability measure on the unit circle. They were introduced by Szegő (1920, 1921, 1939). In mathematics, orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle in the complex plane, for some probability measure on the unit circle. They were introduced by Szegő (1920, 1921, 1939). Suppose that μ {displaystyle mu } is a probability measure on the unit circle in the complex plane, whose support is not finite. The orthogonal polynomials associated to μ {displaystyle mu } are the polynomials Φ n ( z ) {displaystyle Phi _{n}(z)} with leading term z n {displaystyle z^{n}} that are orthogonal with respect to the measure μ {displaystyle mu } .