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- Associated_Legendre_polynomials abstract "In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equationor equivalentlywhere the indices ℓ and m (which are integers) are referred to as the degree and order of the associated Legendre polynomial respectively. This equation has nonzero solutions that are nonsingular on [−1, 1] only if ℓ and m are integers with 0 ≤ m ≤ ℓ, or with trivially equivalent negative values. When in addition m is even, the function is a polynomial. When m is zero and ℓ integer, these functions are identical to the Legendre polynomials. In general, when ℓ and m are integers, the regular solutions are sometimes called "associated Legendre polynomials", even though they are not polynomials when m is odd. The fully general class of functions with arbitrary real or complex values of ℓ and m are Legendre functions. In that case the parameters are usually labelled with Greek letters.The Legendre ordinary differential equation is frequently encountered in physics and other technical fields. In particular, it occurs when solving Laplace's equation (and related partial differential equations) in spherical coordinates. Associated Legendre polynomials play a vital role in the definition of spherical harmonics.".
- Associated_Legendre_polynomials wikiPageExternalLink 0507007.
- Associated_Legendre_polynomials wikiPageExternalLink AssociatedLegendrePolynomial.html.
- Associated_Legendre_polynomials wikiPageExternalLink LegendrePolynomial.html.
- Associated_Legendre_polynomials wikiPageID "1062015".
- Associated_Legendre_polynomials wikiPageRevisionID "596150897".
- Associated_Legendre_polynomials b "ℓ".
- Associated_Legendre_polynomials first "René F.".
- Associated_Legendre_polynomials first "Roderick S. C.".
- Associated_Legendre_polynomials first "Roelof".
- Associated_Legendre_polynomials first "T. M.".
- Associated_Legendre_polynomials first "Tom H.".
- Associated_Legendre_polynomials hasPhotoCollection Associated_Legendre_polynomials.
- Associated_Legendre_polynomials id "14".
- Associated_Legendre_polynomials id "18".
- Associated_Legendre_polynomials last "Dunster".
- Associated_Legendre_polynomials last "Koekoek".
- Associated_Legendre_polynomials last "Koornwinder".
- Associated_Legendre_polynomials last "Swarttouw".
- Associated_Legendre_polynomials last "Wong".
- Associated_Legendre_polynomials p "m".
- Associated_Legendre_polynomials title "Legendre and Related Functions".
- Associated_Legendre_polynomials title "Orthogonal Polynomials".
- Associated_Legendre_polynomials subject Category:Atomic_physics.
- Associated_Legendre_polynomials subject Category:Orthogonal_polynomials.
- Associated_Legendre_polynomials type Abstraction100002137.
- Associated_Legendre_polynomials type Function113783816.
- Associated_Legendre_polynomials type MathematicalRelation113783581.
- Associated_Legendre_polynomials type OrthogonalPolynomials.
- Associated_Legendre_polynomials type Polynomial105861855.
- Associated_Legendre_polynomials type Relation100031921.
- Associated_Legendre_polynomials comment "In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equationor equivalentlywhere the indices ℓ and m (which are integers) are referred to as the degree and order of the associated Legendre polynomial respectively. This equation has nonzero solutions that are nonsingular on [−1, 1] only if ℓ and m are integers with 0 ≤ m ≤ ℓ, or with trivially equivalent negative values. When in addition m is even, the function is a polynomial.".
- Associated_Legendre_polynomials label "Associated Legendre polynomials".
- Associated_Legendre_polynomials label "Funzione associata di Legendre".
- Associated_Legendre_polynomials label "Função de Legendre".
- Associated_Legendre_polynomials label "Geassocieerde Legendrepolynoom".
- Associated_Legendre_polynomials label "Polinomios asociados de Legendre".
- Associated_Legendre_polynomials label "Stowarzyszone funkcje Legendre'a".
- Associated_Legendre_polynomials label "Zugeordnete Legendrepolynome".
- Associated_Legendre_polynomials label "ルジャンドルの微分方程式".
- Associated_Legendre_polynomials label "伴随勒让德多项式".
- Associated_Legendre_polynomials sameAs Zugeordnete_Legendrepolynome.
- Associated_Legendre_polynomials sameAs Polinomios_asociados_de_Legendre.
- Associated_Legendre_polynomials sameAs Funzione_associata_di_Legendre.
- Associated_Legendre_polynomials sameAs ルジャンドルの微分方程式.
- Associated_Legendre_polynomials sameAs 르장드르_연관_함수.
- Associated_Legendre_polynomials sameAs Geassocieerde_Legendrepolynoom.
- Associated_Legendre_polynomials sameAs Stowarzyszone_funkcje_Legendre'a.
- Associated_Legendre_polynomials sameAs Função_de_Legendre.
- Associated_Legendre_polynomials sameAs m.042nzg.
- Associated_Legendre_polynomials sameAs Q228376.
- Associated_Legendre_polynomials sameAs Q228376.
- Associated_Legendre_polynomials sameAs Associated_Legendre_polynomials.
- Associated_Legendre_polynomials wasDerivedFrom Associated_Legendre_polynomials?oldid=596150897.
- Associated_Legendre_polynomials isPrimaryTopicOf Associated_Legendre_polynomials.