Stokes phenomenon
E620767
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Stokes phenomenon canonical | 5 |
| Stokes multipliers | 1 |
| Stokes phenomena | 1 |
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.
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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.
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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.
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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 ⓘ 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
ⓘ
linked to:
Stokes phenomenon
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
ⓘ
linked to:
George Stokes
|
| namedAfter |
George Gabriel Stokes
ⓘ
linked to:
George Stokes
|
| occursIn | complex plane ⓘ |
| relatedTo |
Borel summation
ⓘ
Stokes lines ⓘ 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
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Stokes phenomenon Description of subject: 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.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.