Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
electromagnetic waves in cylindrical structures
heat conduction in a cylinder vibration of a circular membrane |
| gptkbp:basisFor |
Bessel functions of the first kind
|
| gptkbp:coefficientFormula |
a_n = (2 / [J_{ν+1}(α_n)]^2) ∫₀¹ x f(x) J_ν(α_n x) dx
|
| gptkbp:expansion |
orthogonal expansion
|
| gptkbp:expansionFormula |
f(x) = Σ a_n J_ν(α_n x)
|
| gptkbp:field |
gptkb:mathematics
applied mathematics mathematical analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Fourier-Bessel series
|
| gptkbp:namedAfter |
gptkb:Friedrich_Bessel
gptkb:Joseph_Fourier |
| gptkbp:orthogonality |
Bessel functions are orthogonal on a finite interval with weight x
|
| gptkbp:parameter |
ν (order of Bessel function)
|
| gptkbp:relatedTo |
gptkb:Bessel_functions
Fourier series |
| gptkbp:usedIn |
problems with cylindrical symmetry
solution of partial differential equations |
| gptkbp:variant |
x in [0,1]
|
| gptkbp:zeros |
α_n are zeros of J_ν(x)
|
| gptkbp:bfsParent |
gptkb:Bessel_functions
|
| gptkbp:bfsLayer |
6
|