Content-Length: 60720 | pFad | https://dlmf.nist.gov/./../././.././././bib/.././7.3#F4

DLMF: §7.3 Graphics ‣ Properties ‣ Chapter 7 Error Functions, Dawson’s and Fresnel Integrals

About the Project

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

§7.3 Graphics

ⓘ

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

Contents

§7.3(i) Real Variable

ⓘ

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

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

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

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

See accompanying text — 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

§7.3(ii) Complex Variable

ⓘ

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

See accompanying text — Figure 7.3.5: $|\operatorname{erf}\left(x+iy\right)|$ , $-3\leq x\leq 3$ , $-3\leq y\leq 3$ . Compare §7.13(i). Magnify 3D Help

See accompanying text — Figure 7.3.6: $|\operatorname{erfc}\left(x+iy\right)|$ , $-3\leq x\leq 3$ , $-3\leq y\leq 3$ . Compare §§7.12(i) and 7.13(ii). Magnify 3D Help

7.2 Definitions 7.4 Symmetry

© 2010–2024 NIST / Disclaimer / Feedback; Version 1.2.3; Release date 2024-12-15.

NIST

Site Privacy Accessibility Privacy Program Copyrights Vulnerability Disclosure No Fear Act Policy FOIA Environmental Policy Scientific Integrity Information Quality Standards Commerce.gov Science.gov USA.gov