Explore: Orthogonal Circle Polynomials

In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after optical physicist Frits Zernike

mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other

mathematics, orthogonal polynomials on the unit circle are families of polynomials that are orthogonal with respect to integration over the unit circle in the

between various types and orders of aberrations. Zernike's orthogonal circle polynomials provided a solution to the long-standing problem of the optimum

Newton polynomial Orthogonal polynomials Orthogonal polynomials on the unit circle Permutation polynomial Racah polynomials Rogers polynomials Rogers–Szegő

generalized Laguerre polynomials, as will be done here (alternatively associated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor

cos(nx) are similar to the monomial basis for polynomials. In the complex case the trigonometric polynomials are spanned by the positive and negative powers

through the midpoint on a first degree polynomial). Low-order polynomials tend to be smooth and high order polynomial curves tend to be "lumpy". To define

self-reciprocal polynomial satisfy ai = an−i for all i. Reciprocal polynomials have several connections with their original polynomials, including: deg

Bernstein polynomials, restricted to the interval [0, 1], became important in the form of Bézier curves. A numerically stable way to evaluate polynomials in