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product of polynomials

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  • 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

  • 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

  • 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

  • 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

  • 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

  • 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

  • Greatest common divisor of two polynomials — Informally, the greatest common divisor (GCD) of two polynomials p ( x ) and q ( x ) is the biggest polynomial that divides evenly into both p ( x ) and q ( x ). The definition is modeled on the concept of the greatest common divisor of two… …   Wikipedia

  • Euler product — In number theory, an Euler product is an infinite product expansion, indexed by prime numbers p , of a Dirichlet series. The name arose from the case of the Riemann zeta function, where such a product representation was proved by Euler.In general …   Wikipedia

  • Continuous q-Jacobi polynomials — In mathematics, the continuous q Jacobi polynomials P(α,β) n(x|q), introduced by Askey Wilson (1985), are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and René F.… …   Wikipedia

  • Moyal product — In mathematics, the Moyal product, named after José Enrique Moyal, is perhaps the best known example of a phase space star product: an associative, non commutative product, ∗, on the functions on ℝ2n, equipped with its Poisson bracket (with a… …   Wikipedia

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