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Fresnel integral

The Fresnel integrals S(x) and C(x), and their auxiliary functions F(x) and G(x) are transcendental functions named after Augustin-Jean Fresnel that are used in optics and are closely related to the error function (erf). They arise in the description of near-field Fresnel diffraction phenomena and are defined through the following integral representations:

Applications, Euler spiral & Properties

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Definition

Euler spiral

Properties

Generalization

Numerical approximation

Applications

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Fresnel integral

Nodes44
Edges43
Triples156
Avg. degree1.95
Density0.045455
Components1

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Fresnel integral

Top relations

related to References · 110
Fresnel integral → Abramowitz, ACM Trans, Akad, Alazah, Algorithm, Applied Mathematics Series, April, Archived, Aurel, Beatty, BF01793638, BF02162153, Bibcode, Boersma, Boisvert, Bulirsch, CA, Calculus Early Transcendentals, Cambridge University Press, Cengage Learning EMEA
related to External links · 20
Fresnel integral → ALGLIB, Archived, Cephes, Cornu Spiral, EMS Press, Encyclopedia, Eric, Faddeeva Package, Fresnel, Fresnel Integrals, Mathematics, MathWorld, Matlab, Python, Retrieved, Roller Coaster Loop Shapes, SciPy, September, Used, Weisstein
related to Euler spiral · 8
Fresnel integral → Bernoulli, Cornu, Euler, Fresnel, From, Leonhard Euler, Marie Alfred Cornu, The Euler
related to Definition · 6
Fresnel integral → Fresnel, Maclaurin, Some, The Fresnel, These, This
related to Gallery · 5
Fresnel integral → ComplexPlot3D, ComplexPlot3DPlot, Fresnel, Mathematica, Plot
related to Generalization · 4
Fresnel integral → For, Fresnel, Gamma, The
has application · 3
Fresnel integral → More, Other, The Fresnel

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fresnel integrals displaystyle spiral sin frac functions cos left right begin end int pi sqrt euler also doi 10 aligned

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SubjectPredicateObjectConfidenceSrc
Fresnel integralhas applicationThe Fresnel0.60section
Fresnel integralhas applicationMore0.60section
Fresnel integralhas applicationOther0.60section
Fresnel integralrelated to DefinitionThe Fresnel0.60section
Fresnel integralrelated to DefinitionMaclaurin0.60section
Fresnel integralrelated to DefinitionSome0.60section
Fresnel integralrelated to DefinitionThis0.60section
Fresnel integralrelated to DefinitionThese0.60section
Fresnel integralrelated to DefinitionFresnel0.60section
Fresnel integralrelated to Euler spiralThe Euler0.60section
Fresnel integralrelated to Euler spiralCornu0.60section
Fresnel integralrelated to Euler spiralLeonhard Euler0.60section

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