modified Bessel function of the first kind, order 0
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:software
|
| gptkbp:alsoKnownAs |
I₀(x)
|
| gptkbp:asymptoticForLargeX |
I₀(x) ~ exp(x)/sqrt(2πx)
|
| gptkbp:definedIn |
I₀(x) = Σ_{k=0}^∞ ( (x/2)^{2k} ) / (k!)^2
|
| gptkbp:differential |
x²y'' + xy' - x²y = 0
|
| gptkbp:domain |
complex numbers
real numbers |
| https://www.w3.org/2000/01/rdf-schema#label |
modified Bessel function of the first kind, order 0
|
| gptkbp:integration |
I₀(x) = (1/π) ∫₀^π exp(x cos θ) dθ
|
| gptkbp:isEvenFunction |
true
|
| gptkbp:namedAfter |
gptkb:Friedrich_Bessel
|
| gptkbp:recurrence |
I₀'(x) = I₁(x)
|
| gptkbp:relatedTo |
gptkb:Bessel_function_of_the_first_kind
gptkb:modified_Bessel_function_of_the_second_kind I₁(x) |
| gptkbp:solvedBy |
gptkb:modified_Bessel's_differential_equation
|
| gptkbp:usedIn |
gptkb:probability_theory
gptkb:signal_processing statistical distributions (e.g., Rice distribution) solutions to heat equation in cylindrical coordinates |
| gptkbp:valueAtZero |
1
|
| gptkbp:bfsParent |
gptkb:von_Mises_distribution
|
| gptkbp:bfsLayer |
7
|