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7 Error Functions, Dawson’s and Fresnel IntegralsProperties

§7.3 Graphics


§7.3(i) Real Variable

See accompanying text
Figure 7.3.1: Complementary error functions erfcx and erfc(10x), -3x3. Magnify
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Figure 7.3.2: Dawson’s integral F(x), -3.5x3.5. Magnify
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Figure 7.3.3: Fresnel integrals C(x) and S(x), 0x4. Magnify
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Figure 7.3.4: |(x)|2, -8x8. Fresnel (1818) introduced the integral (x) in his study of the interference pattern at the edge of a shadow. He observed that the intensity distribution is given by |(x)|2. Magnify

§7.3(ii) Complex Variable

Figure 7.3.5: |erf(x+iy)|, -3x3, -3y3. Compare §7.13(i). Magnify
Figure 7.3.6: |erfc(x+iy)|, -3x3, -3y3. Compare §§7.12(i) and 7.13(ii). Magnify