7 Error Functions, Dawson’s and Fresnel Integrals Properties 7.2 Definitions 7.4 Symmetry

§7.3 Graphics

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Permalink:: http://dlmf.nist.gov/7.3
See also:: Annotations for Ch.7

§7.3(i) Real Variable
§7.3(ii) Complex Variable

§7.3(i) Real Variable

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Notes:: These graphs were produced at NIST.
Permalink:: http://dlmf.nist.gov/7.3.i
See also:: Annotations for §7.3 and Ch.7

Figure 7.3.1: Complementary error functions $\operatorname{erfc}x$ and $\operatorname{erfc}\left(10x\right)$ , $-3\leq x\leq 3$ . Magnify

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Symbols:: $\operatorname{erfc}\NVar{z}$ : complementary error function and : real variable
Keywords:: error functions, graphics
Permalink:: http://dlmf.nist.gov/7.3.F1
Encodings:: pdf, png
See also:: Annotations for §7.3(i), §7.3 and Ch.7

Figure 7.3.2: Dawson’s integral $F\left(x\right)$ , $-3.5\leq x\leq 3.5$ . Magnify

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Symbols:: $F\left(\NVar{z}\right)$ : Dawson’s integral and : real variable
Keywords:: Dawson’s integral, graphics
Permalink:: http://dlmf.nist.gov/7.3.F2
Encodings:: pdf, png
See also:: Annotations for §7.3(i), §7.3 and Ch.7

Figure 7.3.3: Fresnel integrals $C\left(x\right)$ and $S\left(x\right)$ , $0\leq x\leq 4$ . Magnify

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Symbols:: $C\left(\NVar{z}\right)$ : Fresnel integral, $S\left(\NVar{z}\right)$ : Fresnel integral and : real variable
Keywords:: Fresnel integrals, Fresnel integrals and Cornu’s spiral, diffraction of light, graphics
Permalink:: http://dlmf.nist.gov/7.3.F3
Encodings:: pdf, png
See also:: Annotations for §7.3(i), §7.3 and Ch.7

Figure 7.3.4: $|\mathcal{F}\left(x\right)|^{2}$ , $-8\leq x\leq 8$ . Fresnel (1818) introduced the integral $\mathcal{F}\left(x\right)$ in his study of the interference pattern at the edge of a shadow. He observed that the intensity distribution is given by ${\left|\mathcal{F}\left(x\right)\right|}^{2}$ . Magnify

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