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Airy function

In mathematics, the Airy function (or Airy function of the first kind) A i ( x ) {\displaystyle \mathbf {Ai({\boldsymbol {x}})} } is a special function named after the British astronomer George Biddell Airy. The function Ai ⁡ ( x ) {\displaystyle \operatorname {Ai} (x)} and the related function B i ( x ) {\displaystyle \mathbf {Bi({\boldsymbol {x}})} }…

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Overview

Definitions

Properties

Asymptotic formulae

Complex arguments

Relation to other special functions

Integration

Fourier transform

Applications

History

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Airy function

Nodes56
Edges55
Triples137
Avg. degree1.96
Density0.035714
Components1

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Airy function

Top relations

related to External links · 25
Airy function → Ai, Airy, Airy Functions, Bi, Boisvert, Cambridge University Press, Charles, Clark, Daniel, EMS Press, Encyclopedia, Eric, Frank, Includes, ISBN, Lozier, Mathematical Functions, Mathematics, MathWorld, MR
related to References · 23
Airy function → Airy, Airy Functions, BP, Cambridge University Press, Flannery, Imperial College Press, ISBN, London, Manuel, MR, New York, Numerical Recipes, Olivier, Press, SA, Scientific Computing, Section, Soares, Teukolsky, The Art
related to Probability · 12
Airy function → Airy, Chernoff's, Due, In, Kardar, KPZ, Parisi, Random, The Airy, Tracy, Widom, Zhang
related to Asymptotic formulae · 10
Airy function → Ai, Airy, As, Bi, For, Gamma, In, Stokes, The, There
related to Fourier transform · 10
Airy function → Ai, Airy, Bi, Ce, Fourier, Let, Then, There, This, Using
related to Properties · 10
Airy function → Ai, Airy, Bi, Gamma, Here, It, The, This, When, Wronskian
related to Caustics · 9
Airy function → Ai, Airy, He, Historically, In, Maslov, The, The Airy, William Hallowes Miller
related to history · 8
Airy function → Ai, Airy, British, British Astronomer Royal, George Biddell Airy, Harold Jeffreys, The, The Airy
related to Relation to other special functions · 8
Airy function → Ai, Airy, Bessel, Bi, For, Here, K1/3, The
related to Complex arguments · 7
Airy function → Ai, Airy, Alternatively, Bi, Finally, The, We

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Important terminology

ai displaystyle bi airy operatorname function frac pi functions left right arg infty equation asymptotic exp sqrt solutions also sin

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Airy functionis asolution to the time-independent Schrödinger equation for a particle confined within a triangular potential well and for a particle in a one-dimensional constant force field0.90text
Airy functionis auniversal local model near a fold caustic0.90text
the Airy processinstance ofthere are central processes constructed in KPZ0.80text
Airy functionrelated to Asymptotic formulaeAs0.60section
Airy functionrelated to Asymptotic formulaeAiry0.60section
Airy functionrelated to Asymptotic formulaeThe0.60section
Airy functionrelated to Asymptotic formulaeStokes0.60section
Airy functionrelated to Asymptotic formulaeFor0.60section
Airy functionrelated to Asymptotic formulaeAi0.60section
Airy functionrelated to Asymptotic formulaeGamma0.60section
Airy functionrelated to Asymptotic formulaeIn0.60section
Airy functionrelated to Asymptotic formulaeThere0.60section

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