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gptkbp:instanceOf
|
gptkb:software
|
|
gptkbp:analyticEverywhere
|
true
|
|
gptkbp:asymptoticBehavior
|
decays for large positive x
oscillates for large negative x
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gptkbp:definedIn
|
partial differential equations
|
|
gptkbp:differentialEquationType
|
second order linear ODE
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gptkbp:domain
|
complex numbers
real numbers
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gptkbp:entireFunction
|
true
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|
gptkbp:evenFunction
|
false
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gptkbp:firstZero
|
-2.3381...
|
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gptkbp:hasCompanionFunction
|
gptkb:Airy_function_Bi(x)
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gptkbp:hasZeros
|
real and negative
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|
https://www.w3.org/2000/01/rdf-schema#label
|
Airy function Ai(x)
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gptkbp:integration
|
(1/π) ∫₀^∞ cos((t³/3) + x t) dt
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|
gptkbp:minimumPressure
|
at x ≈ -1.0188
|
|
gptkbp:namedAfter
|
gptkb:George_Biddell_Airy
|
|
gptkbp:orthogonalWithRespectTo
|
certain weight functions
|
|
gptkbp:relatedTo
|
gptkb:Bessel_functions
|
|
gptkbp:seriesExpansion
|
Σ_{n=0}^∞ (3^{-2n} x^{3n})/(n! Γ(n + 2/3))
|
|
gptkbp:solvedBy
|
y'' - x y = 0
|
|
gptkbp:usedIn
|
gptkb:optics
gptkb:Stokes_phenomenon
quantum mechanics
diffraction theory
|
|
gptkbp:valueAtZero
|
1/(3^{2/3} Γ(2/3))
|
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gptkbp:bfsParent
|
gptkb:Airy_differential_equation
|
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gptkbp:bfsLayer
|
6
|