Stokes phenomenon

E620767

mathematical concept phenomenon in asymptotic analysis

The Stokes phenomenon is a concept in asymptotic analysis describing the abrupt change in the behavior of asymptotic expansions of functions as one crosses certain lines, called Stokes lines, in the complex plane.

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All labels observed (1)

Label	Occurrences
Stokes phenomenon canonical	3

How this entity was disambiguated

This entity first appeared as the object of triple T6788236 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Stokes phenomenon
Context triple: [George Gabriel Stokes, knownFor, Stokes phenomenon]

A. Fuchsian singularity
A Fuchsian singularity is a type of regular singular point of a linear differential equation in the complex plane, characterized by well-controlled (typically polynomially bounded) behavior of solutions near the singularity.
B. Asymptotic Methods in Analysis
Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
C. Fuchsian differential equation
A Fuchsian differential equation is a type of linear ordinary differential equation characterized by having only regular singular points, extensively studied in complex analysis and the theory of special functions.
D. Painlevé–Kruskal theorem
The Painlevé–Kruskal theorem is a result in the theory of nonlinear differential equations that characterizes integrability through the analytic structure of their solutions, particularly via the Painlevé property.
E. Borel summation
Borel summation is a mathematical technique that assigns finite values to certain divergent series by transforming and analytically continuing their associated power series.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Stokes phenomenon
Target entity description: The Stokes phenomenon is a concept in asymptotic analysis describing the abrupt change in the behavior of asymptotic expansions of functions as one crosses certain lines, called Stokes lines, in the complex plane.

A. Fuchsian singularity
A Fuchsian singularity is a type of regular singular point of a linear differential equation in the complex plane, characterized by well-controlled (typically polynomially bounded) behavior of solutions near the singularity.
B. Asymptotic Methods in Analysis
Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
C. Fuchsian differential equation
A Fuchsian differential equation is a type of linear ordinary differential equation characterized by having only regular singular points, extensively studied in complex analysis and the theory of special functions.
D. Painlevé–Kruskal theorem
The Painlevé–Kruskal theorem is a result in the theory of nonlinear differential equations that characterizes integrability through the analytic structure of their solutions, particularly via the Painlevé property.
E. Borel summation
Borel summation is a mathematical technique that assigns finite values to certain divergent series by transforming and analytically continuing their associated power series.
F. None of above. chosen

Statements (48)

Predicate	Object
instanceOf	mathematical concept ⓘ phenomenon in asymptotic analysis ⓘ
appearsIn	Airy function asymptotics ⓘ Bessel function asymptotics ⓘ Gamma function asymptotics ⓘ WKB approximation NERFINISHED ⓘ asymptotics of special functions ⓘ singular perturbation theory ⓘ solutions of linear differential equations with large parameter ⓘ
characterizedBy	change of dominant asymptotic contribution ⓘ discontinuous change in asymptotic coefficients’ effective contribution ⓘ
concerns	analytic continuation of functions ⓘ asymptotic expansion of functions ⓘ sectorial behavior of asymptotic series ⓘ
describes	abrupt change in asymptotic expansions ⓘ switching on and off of exponentially small terms ⓘ
field	applied mathematics ⓘ asymptotic analysis ⓘ complex analysis ⓘ
formalizedBy	Stokes multipliers NERFINISHED ⓘ connection matrices ⓘ
hasExample	change of Airy function asymptotics across arg(z)=±2π/3 ⓘ change of Bessel function asymptotics across specific rays in the complex plane ⓘ
hasKeyConcept	Stokes line ⓘ Stokes multiplier ⓘ asymptotic sector ⓘ connection formula ⓘ exponentially small terms ⓘ
hasProperty	asymptotic expansion changes sectorially ⓘ depends on argument of complex variable ⓘ occurs across specific rays from singular points ⓘ
historicalPeriod	19th century ⓘ
introducedBy	George Gabriel Stokes NERFINISHED ⓘ
namedAfter	George Gabriel Stokes NERFINISHED ⓘ
occursIn	complex plane ⓘ
relatedTo	Borel summation NERFINISHED ⓘ Stokes lines NERFINISHED ⓘ analytic continuation across branch cuts ⓘ anti-Stokes lines ⓘ divergent series ⓘ resurgent analysis ⓘ saddle point method ⓘ steepest descent paths ⓘ turning points in differential equations ⓘ
studiedIn	asymptotic theory of differential equations ⓘ geometric theory of differential equations ⓘ
usedFor	accurate asymptotic description in different complex sectors ⓘ understanding switching behavior of asymptotic terms ⓘ

How these facts were elicited

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Stokes → knownFor → Stokes phenomenon ⓘ

subject surface form: George Gabriel Stokes

Stokes → hasEponym → Stokes phenomenon ⓘ

George Gabriel → hasHonorNamedAfter → Stokes phenomenon ⓘ