Statements (39)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
partial differential equations |
| gptkbp:appliesTo |
gptkb:Laguerre_polynomials
gptkb:Legendre_polynomials gptkb:Chebyshev_polynomials gptkb:Bessel_functions gptkb:Hermite_polynomials orthogonal polynomials |
| gptkbp:category |
Ordinary differential equations
Mathematical physics Spectral theory |
| gptkbp:describes |
eigenvalue problem for linear differential operators
|
| gptkbp:field |
gptkb:mathematics
mathematical physics |
| gptkbp:form |
(d/dx)[p(x) dy/dx] + [q(x) + λw(x)]y = 0
|
| gptkbp:function |
coefficient function p(x)
coefficient function q(x) weight function w(x) |
| gptkbp:generalizes |
Fourier analysis
|
| https://www.w3.org/2000/01/rdf-schema#label |
Sturm–Liouville problem
|
| gptkbp:involves |
boundary conditions
second-order linear differential equation |
| gptkbp:namedAfter |
gptkb:Joseph_Liouville
gptkb:Jacques_Charles_François_Sturm |
| gptkbp:parameter |
eigenvalue λ
|
| gptkbp:relatedTo |
gptkb:Hilbert_space
self-adjoint operators spectral theory |
| gptkbp:solvedBy |
eigenvalues
eigenfunctions orthogonal functions |
| gptkbp:studiedBy |
19th century
|
| gptkbp:usedIn |
Fourier series
heat conduction partial differential equations quantum mechanics vibrations analysis |
| gptkbp:bfsParent |
gptkb:Gelfand–Levitan_equation
|
| gptkbp:bfsLayer |
5
|