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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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 ⓘ

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 ⓘ

subject surface form: George Gabriel Stokes