Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
special functions
|
| gptkbp:domain |
complex numbers
real numbers |
| gptkbp:firstPublished |
1782
|
| gptkbp:hasGeneratingFunction |
(1-2xt+t^2)^{-1/2}
|
| https://www.w3.org/2000/01/rdf-schema#label |
Legendre functions
|
| gptkbp:includes |
gptkb:Legendre_polynomials
associated Legendre functions |
| gptkbp:namedAfter |
gptkb:Adrien-Marie_Legendre
|
| gptkbp:notation |
P_n(x)
P_n^m(x) |
| gptkbp:orthogonal |
yes
|
| gptkbp:orthogonalOn |
interval [-1, 1]
|
| gptkbp:relatedTo |
spherical harmonics
hypergeometric functions |
| gptkbp:satisfies |
recurrence relations
|
| gptkbp:solvedBy |
gptkb:Legendre_differential_equation
|
| gptkbp:usedIn |
mathematical physics
quantum mechanics potential theory |
| gptkbp:bfsParent |
gptkb:hypergeometric_function
|
| gptkbp:bfsLayer |
7
|