modified Bessel function of the first kind, order 1
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:software
|
| gptkbp:affiliatedWith |
gptkb:modified_Bessel_functions
|
| gptkbp:alsoKnownAs |
I₁(x)
|
| gptkbp:asymptoticForLargeX |
I₁(x) ~ e^x / sqrt(2πx)
|
| gptkbp:domain |
complex numbers
|
| gptkbp:hasSeriesExpansion |
I₁(x) = Σ_{k=0}^∞ [ (x/2)^{2k+1} / (k! Γ(k+2)) ]
|
| https://www.w3.org/2000/01/rdf-schema#label |
modified Bessel function of the first kind, order 1
|
| gptkbp:isEvenFunction |
false
|
| gptkbp:isOddFunction |
true
|
| gptkbp:namedAfter |
gptkb:Friedrich_Bessel
|
| gptkbp:order |
1
|
| gptkbp:range |
complex numbers
|
| gptkbp:recurrence |
I₁'(x) = I₀(x) - (1/x)I₁(x)
I₁(x) = (I₀'(x) + I₂'(x))/2 |
| gptkbp:satisfies |
gptkb:modified_Bessel_differential_equation
|
| gptkbp:solvedBy |
x²y'' + xy' - (x² + 1²)y = 0
|
| gptkbp:usedIn |
gptkb:probability_theory
engineering mathematical physics solutions to partial differential equations |
| gptkbp:valueAtZero |
0
|
| gptkbp:bfsParent |
gptkb:von_Mises_distribution
|
| gptkbp:bfsLayer |
7
|