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

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

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

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

ISBN 0-07-054233-3, MR 0344043, Zbl 0278.26001 Simon, Barry (2005), Orthogonal polynomials on the unit circle. Part 1. Classical theory, American Mathematical Society...

palindromic polynomials include cyclotomic polynomials and Eulerian polynomials. If a is a root of a polynomial that is either palindromic or antipalindromic...

Academic Press. ISBN 0-12-305340-4. Simon, Barry (2005). Orthogonal polynomials on the unit circle. Part 1. Classical theory. American Mathematical Society...

mathematics, the Bessel polynomials are an orthogonal sequence of polynomials. There are a number of different but closely related definitions. The definition...

{\gamma _{j}}}+{\frac {1}{zf_{j+1}(z)}}}}.} Orthogonal polynomials on the unit circle Szegő polynomial Schur, J. (1918), "Über die Potenzreihen, die...

Bochner's theorem Hamburger moment problem Moment problem Orthogonal polynomials on the unit circle Spectral measure Schur class Szegő limit theorems Wiener's...

the mathematical field of numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials...

Mathematics, EMS Press, 2001 [1994] Simon, Barry (2005). Orthogonal polynomials on the unit circle. Part 1. Classical theory. American Mathematical Society...

Society, 1999. ISBN 0821819178 2015 – Barry Simon for his Orthogonal Polynomials on the Unit Circle, American Mathematical Society, 2005. ISBN 9780821834466...

the American Mathematical Society. 124 (7): 2073–2080. doi:10.1090/S0002-9939-96-03465-X. ISSN 0002-9939. Simon, Barry (2005). Orthogonal polynomials...

magnetic fields, the semi-classical limit, the singular continuous spectrum, random and ergodic Schrödinger operators, orthogonal polynomials, and non-selfadjoint...

Table of spherical harmonics Vector spherical harmonics Zernike polynomials Jacobi polynomials Atomic orbital A historical account of various approaches to...

Applications to Orthogonal Polynomials. In: V. G. Ganzha, E. W. Mayr and E. V. Vorozhtsov (Editors): Proceedings of the 10th International Workshop on Computer...

are frequently used to study orthogonal polynomials, because different families of orthogonal polynomials are orthogonal with respect to different weighting...

equation) in which the two sides are polynomials. The sides of a polynomial equation contain one or more terms. For example, the equation A x 2 + B x...

vertices on a common circle Pythagoras in popular culture Pythagorean expectation Pythagorean hodograph curve – determined by polynomials that obey the Pythagorean...

symmetry group is the orthogonal group O(2,R). The group of rotations alone is the circle group T. All circles are similar. A circle circumference and radius...

d\varphi _{n-1}.} The natural choice of an orthogonal basis over the angular coordinates is a product of ultraspherical polynomials, ∫ 0 π sin n − j −...

is the rotation group SO(3). The set of all orthogonal matrices of size n with determinant +1 or −1 is a representation of the (general) orthogonal group...

with all eigenvalues being unit modulus, real, and imaginary, respectively. Likewise, among real matrices, all orthogonal, symmetric, and skew-symmetric...

low-frequency components. The Bernstein polynomials of a fixed degree m are a family of m+1 linearly independent single-variable polynomials that are a partition...

concentric circles Area of a disk – Concept in geometryPages displaying short descriptions of redirect targets Bipolar coordinates – 2-dimensional orthogonal coordinate...

Archive, University of St Andrews Simon, Barry (2005), Orthogonal polynomials on the unit circle. Part 1. Classical theory, American Mathematical Society...

Z[x], or any polynomial f ∈ k[x1, ..., xn]. There is a circle of idempotents in the ring of split-quaternions. Split quaternions have the structure of...

mathematics, the Rogers–Szegő polynomials are a family of polynomials orthogonal on the unit circle introduced by Szegő (1926), who was inspired by the continuous...

f(z)=z^{2}} the Julia set is the unit circle and on this the iteration is given by doubling of angles (an operation that is chaotic on the points whose...