polynomials

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• polynomials — pol·y·no·mi·al || ‚pÉ‘lɪ nəʊmɪəl /‚pÉ’ n. algebraic expression that is the sum of two or more constants multiplied by variables with exponents (Mathematics) …   English contemporary dictionary

• Classical orthogonal polynomials — In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical… …   Wikipedia

• Orthogonal polynomials — In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the… …   Wikipedia

• Chebyshev polynomials — Not to be confused with discrete Chebyshev polynomials. In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev,[1] are a sequence of orthogonal polynomials which are related to de Moivre s formula and which can be defined… …   Wikipedia

• Hermite polynomials — In mathematics, the Hermite polynomials are a classical orthogonal polynomial sequence that arise in probability, such as the Edgeworth series; in combinatorics, as an example of an Appell sequence, obeying the umbral calculus; in numerical… …   Wikipedia

• Macdonald polynomials — In mathematics, Macdonald polynomials Pλ(x; t,q) are a family of orthogonal polynomials in several variables, introduced by Macdonald (1987). Macdonald originally associated his polynomials with weights λ of finite root systems and used just …   Wikipedia

• Legendre polynomials — Note: People sometimes refer to the more general associated Legendre polynomials as simply Legendre polynomials . In mathematics, Legendre functions are solutions to Legendre s differential equation::{d over dx} left [ (1 x^2) {d over dx} P n(x)… …   Wikipedia

• Bernoulli polynomials — In mathematics, the Bernoulli polynomials occur in the study of many special functions and in particular the Riemann zeta function and the Hurwitz zeta function. This is in large part because they are an Appell sequence, i.e. a Sheffer sequence… …   Wikipedia

• Laguerre polynomials — In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 ndash; 1886), are the canonical solutions of Laguerre s equation::x,y + (1 x),y + n,y = 0,which is a second order linear differential equation.This equation has… …   Wikipedia

• Bell polynomials — In combinatorial mathematics, the Bell polynomials, named in honor of Eric Temple Bell, are a triangular array of polynomials given by the sum extending over all sequences j1, j2, j3, ..., jn−k+1 of non negative integers such that …   Wikipedia

• Zernike polynomials — Plots of the values in the unit disk.In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after Frits Zernike, they play an important role in geometrical optics. DefinitionsThere are… …   Wikipedia