modified Bessel function of the second kind
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:software
|
| gptkbp:alsoKnownAs |
gptkb:Macdonald_function
|
| gptkbp:definedIn |
solution to the modified Bessel's differential equation
|
| gptkbp:domain |
complex numbers
real numbers |
| gptkbp:hasAsymptoticForm |
decays exponentially for large arguments
|
| gptkbp:hasSeriesExpansion |
yes
|
| https://www.w3.org/2000/01/rdf-schema#label |
modified Bessel function of the second kind
|
| gptkbp:integration |
Kν(x) = ∫₀^∞ exp(-x cosh t) cosh(ν t) dt
|
| gptkbp:isEvenFunctionOfOrder |
Kν(x) = K-ν(x)
|
| gptkbp:isRealValuedFor |
real positive arguments
|
| gptkbp:isSingularAt |
x = 0 for ν ≠ 0
|
| gptkbp:namedAfter |
gptkb:William_Thomson,_1st_Baron_Kelvin
|
| gptkbp:order |
ν (nu)
|
| gptkbp:recurrence |
Kν-1(x) - Kν+1(x) = 2ν/x Kν(x)
|
| gptkbp:relatedTo |
gptkb:modified_Bessel_function_of_the_first_kind
|
| gptkbp:satisfies |
Kν(x) = K-ν(x)
|
| gptkbp:symbol |
Kν(x)
|
| gptkbp:usedIn |
gptkb:probability_theory
engineering mathematical physics |
| gptkbp:bfsParent |
gptkb:Bessel_K
|
| gptkbp:bfsLayer |
7
|