Fresnel integral
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Wikidata facts
- Subclass of
- special function
- Named after
- Augustin-Jean Fresnel
- Image
- Fresnel Integrals (Unnormalised).svg
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- Commons category
- Fresnel integrals
- maintained by WikiProject
- WikiProject Mathematics
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Encyclopedic overview
Plots of S(x) and C(x). The maximum of C(x) is about 0.977451424. If the integrands of S and C were defined using π/2t instead of t, then the image would be scaled vertically and horizontally (see below).
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:
Excerpted from Wikipedia’s “Fresnel integral” article, available under the CC BY-SA 4.0 licence.