Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
orthogonal polynomials
|
| gptkbp:category |
gptkb:mathematical_concept
gptkb:software |
| gptkbp:definedIn |
interval [-1, 1]
|
| gptkbp:degree |
n (non-negative integer)
|
| gptkbp:firstAppearance |
19th century
|
| gptkbp:hasSpecialCase |
gptkb:Gegenbauer_polynomials
gptkb:Legendre_polynomials gptkb:Chebyshev_polynomials gptkb:hypergeometric_function |
| https://www.w3.org/2000/01/rdf-schema#label |
Jacobi polynomials
|
| gptkbp:namedAfter |
gptkb:Carl_Gustav_Jacob_Jacobi
|
| gptkbp:notation |
P_n^{(alpha, beta)}(x)
|
| gptkbp:orthogonalWithRespectTo |
weight function (1-x)^alpha (1+x)^beta
|
| gptkbp:parameter |
alpha
beta |
| gptkbp:recurrence |
yes
|
| gptkbp:satisfies |
second-order differential equation
|
| gptkbp:usedIn |
numerical analysis
approximation theory spectral methods |
| gptkbp:bfsParent |
gptkb:Generalized_Polynomial_Chaos
gptkb:Meixner–Pollaczek_polynomials |
| gptkbp:bfsLayer |
6
|