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gptkbp:instanceOf
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gptkb:partial_differential_equations
gptkb:mathematical_concept
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gptkbp:appliesTo
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gptkb:orthogonal_polynomials
gptkb:Laguerre_polynomials
gptkb:Legendre_polynomials
gptkb:Chebyshev_polynomials
gptkb:Bessel_functions
gptkb:Hermite_polynomials
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gptkbp:category
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Ordinary differential equations
Mathematical physics
Spectral theory
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gptkbp:describes
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eigenvalue problem for linear differential operators
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gptkbp:field
|
gptkb:mathematics
mathematical physics
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gptkbp:form
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(d/dx)[p(x) dy/dx] + [q(x) + λw(x)]y = 0
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gptkbp:function
|
coefficient function p(x)
coefficient function q(x)
weight function w(x)
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gptkbp:generalizes
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Fourier analysis
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gptkbp:involves
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boundary conditions
second-order linear differential equation
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gptkbp:namedAfter
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gptkb:Joseph_Liouville
gptkb:Jacques_Charles_François_Sturm
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gptkbp:parameter
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eigenvalue λ
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gptkbp:relatedTo
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gptkb:Hilbert_space
self-adjoint operators
spectral theory
|
|
gptkbp:solvedBy
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eigenvalues
eigenfunctions
orthogonal functions
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gptkbp:studiedBy
|
gptkb:19th_century
|
|
gptkbp:usedIn
|
gptkb:partial_differential_equations
Fourier series
heat conduction
quantum mechanics
vibrations analysis
|
|
gptkbp:bfsParent
|
gptkb:Gelfand–Levitan_equation
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gptkbp:bfsLayer
|
8
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http://www.w3.org/2000/01/rdf-schema#label
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Sturm–Liouville problem
|