Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:software
|
| gptkbp:alsoKnownAs |
gptkb:modified_Bessel_function_of_the_first_kind
|
| gptkbp:application |
gptkb:probability_theory
gptkb:signal_processing engineering heat conduction mathematical physics wave propagation |
| gptkbp:asymptoticBehavior |
Iₙ(x) ~ (e^x/√(2πx)) as x→∞
|
| gptkbp:differential |
x²y'' + xy' - (x² + n²)y = 0
|
| gptkbp:domain |
complex numbers
|
| https://www.w3.org/2000/01/rdf-schema#label |
I-Bessel function
|
| gptkbp:integration |
Iₙ(x) = (1/π) ∫₀^π e^{x cos θ} cos(nθ) dθ
|
| gptkbp:namedAfter |
gptkb:Friedrich_Bessel
|
| gptkbp:notation |
Iₙ(x)
|
| gptkbp:order |
real or complex number
|
| gptkbp:orthogonality |
not generally orthogonal
|
| gptkbp:recurrence |
Iₙ₋₁(x) - Iₙ₊₁(x) = (2n/x)Iₙ(x)
|
| gptkbp:relatedTo |
gptkb:Bessel_function_of_the_first_kind
|
| gptkbp:satisfies |
gptkb:modified_Bessel's_differential_equation
|
| gptkbp:seriesExpansion |
Iₙ(x) = Σ_{k=0}^∞ (1/k!Γ(n+k+1)) (x/2)^{n+2k}
|
| gptkbp:bfsParent |
gptkb:modified_Bessel_function_of_the_first_kind
|
| gptkbp:bfsLayer |
8
|