special function defined by an integral
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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:
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Discovered by embedding cosine similarity (sentence-transformers MiniLM, 384-dim).