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- Laguerre_polynomials abstract "In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 – 1886),are solutions of Laguerre's equation: which is a second-order linear differential equation. This equation has nonsingular solutions only if n is a non-negative integer. The associated Laguerre polynomials (alternatively, but rarely, named Sonin polynomials, after their inventor N. Y. Sonin) are solutions of The Laguerre polynomials are also used for Gaussian quadrature to numerically compute integrals of the form These polynomials, usually denoted L0, L1, ..., are a polynomial sequence which may be defined by the Rodrigues formula,reducing to the closed form of a following section.They are orthogonal polynomials with respect to an inner product The sequence of Laguerre polynomials n! Ln is a Sheffer sequence, d⁄dx Ln = (d⁄dx−1) Ln−1.The Rook polynomials in combinatorics are more or less the same as Laguerre polynomials, up to elementary changes of variables.The Laguerre polynomials arise in quantum mechanics, in the radial part of the solutionof the Schrödinger equation for a one-electron atom. They also describe the static Wigner functions of oscillator systems in quantum mechanics in phase space. They further enter in the quantum mechanics of the 3D isotropic harmonic oscillator.Physicists sometimes use a definition for the Laguerre polynomials which is larger by a factor of n! than the definition used here. (Likewise, some physicist may use somewhat different definitions of the so-called associated Laguerre polynomials.)".
- Laguerre_polynomials thumbnail Laguerre_poly.svg?width=300.
- Laguerre_polynomials wikiPageExternalLink LaguerrePolynomial.html.
- Laguerre_polynomials wikiPageExternalLink hydrofin.
- Laguerre_polynomials wikiPageID "943917".
- Laguerre_polynomials wikiPageRevisionID "601589495".
- Laguerre_polynomials b "n".
- Laguerre_polynomials first "René F.".
- Laguerre_polynomials first "Roderick S. C.".
- Laguerre_polynomials first "Roelof".
- Laguerre_polynomials first "Tom H.".
- Laguerre_polynomials hasPhotoCollection Laguerre_polynomials.
- Laguerre_polynomials id "18".
- Laguerre_polynomials id "LaguerrePolynomial".
- Laguerre_polynomials id "p/l057310".
- Laguerre_polynomials last "Koekoek".
- Laguerre_polynomials last "Koornwinder".
- Laguerre_polynomials last "Swarttouw".
- Laguerre_polynomials last "Wong".
- Laguerre_polynomials p "α".
- Laguerre_polynomials title "Laguerre polynomial".
- Laguerre_polynomials title "Laguerre polynomials".
- Laguerre_polynomials title "Orthogonal Polynomials".
- Laguerre_polynomials subject Category:Orthogonal_polynomials.
- Laguerre_polynomials subject Category:Polynomials.
- Laguerre_polynomials subject Category:Special_hypergeometric_functions.
- Laguerre_polynomials type Abstraction100002137.
- Laguerre_polynomials type Function113783816.
- Laguerre_polynomials type MathematicalRelation113783581.
- Laguerre_polynomials type OrthogonalPolynomials.
- Laguerre_polynomials type Polynomial105861855.
- Laguerre_polynomials type Polynomials.
- Laguerre_polynomials type Relation100031921.
- Laguerre_polynomials type SpecialHypergeometricFunctions.
- Laguerre_polynomials comment "In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834 – 1886),are solutions of Laguerre's equation: which is a second-order linear differential equation. This equation has nonsingular solutions only if n is a non-negative integer. The associated Laguerre polynomials (alternatively, but rarely, named Sonin polynomials, after their inventor N. Y.".
- Laguerre_polynomials label "Laguerre polynomials".
- Laguerre_polynomials label "Laguerre-Polynome".
- Laguerre_polynomials label "Laguerre-polynoom".
- Laguerre_polynomials label "Polinomi di Laguerre".
- Laguerre_polynomials label "Polinomios de Laguerre".
- Laguerre_polynomials label "Polinômios de Laguerre".
- Laguerre_polynomials label "Polynôme de Laguerre".
- Laguerre_polynomials label "Wielomiany Laguerre'a".
- Laguerre_polynomials label "Многочлены Лагерра".
- Laguerre_polynomials label "ラゲールの陪多項式".
- Laguerre_polynomials label "拉盖尔多项式".
- Laguerre_polynomials sameAs Laguerrovy_polynomy.
- Laguerre_polynomials sameAs Laguerre-Polynome.
- Laguerre_polynomials sameAs Polinomios_de_Laguerre.
- Laguerre_polynomials sameAs Polynôme_de_Laguerre.
- Laguerre_polynomials sameAs Polinomi_di_Laguerre.
- Laguerre_polynomials sameAs ラゲールの陪多項式.
- Laguerre_polynomials sameAs 라게르_다항식.
- Laguerre_polynomials sameAs Laguerre-polynoom.
- Laguerre_polynomials sameAs Wielomiany_Laguerre'a.
- Laguerre_polynomials sameAs Polinômios_de_Laguerre.
- Laguerre_polynomials sameAs m.03s2d3.
- Laguerre_polynomials sameAs Q1124546.
- Laguerre_polynomials sameAs Q1124546.
- Laguerre_polynomials sameAs Laguerre_polynomials.
- Laguerre_polynomials wasDerivedFrom Laguerre_polynomials?oldid=601589495.
- Laguerre_polynomials depiction Laguerre_poly.svg.
- Laguerre_polynomials isPrimaryTopicOf Laguerre_polynomials.