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1: 34.9 Graphical Method

§34.9 Graphical Method

►The graphical method establishes a one-to-one correspondence between an analytic expression and a diagram by assigning a graphical symbol to each function and operation of the analytic expression. …For specific examples of the graphical method of representing sums involving the $\mathit{3}j,\mathit{6}j$, and $\mathit{9}j$ symbols, see Varshalovich et al. (1988, Chapters 11, 12) and Lehman and O’Connell (1973, §3.3).

2: 5.3 Graphics

§5.3 Graphics

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Figure 5.3.1: $\mathrm{\Gamma }\left(x\right)$ and $1/\mathrm{\Gamma }\left(x\right)$. … Magnify

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Figure 5.3.3: $\psi \left(x\right)$. Magnify

… ►In the graphics shown in this subsection, both the height and color correspond to the absolute value of the function. … ►

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Figure 5.3.6: $|\psi \left(x+\mathrm{i}y\right)|$. Magnify 3D Help

3: 6.3 Graphics

§6.3 Graphics

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Figure 6.3.1: The exponential integrals $E_1\left(x\right)$ and $\mathrm{Ei}\left(x\right)$, . Magnify

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Figure 6.3.2: The sine and cosine integrals $\mathrm{Si}\left(x\right),\mathrm{Ci}\left(x\right)$, $0\le x\le 15$. Magnify

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Figure 6.3.3: $|E_1\left(x+\mathrm{i}y\right)|$, $-4\le x\le 4$, $-4\le y\le 4$. … Magnify 3D Help

4: 4.29 Graphics

§4.29 Graphics

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§4.29(i) Real Arguments

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Figure 4.29.6: Principal values of $\mathrm{arccsch}x$ and $\mathrm{arcsech}x$. … Magnify

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§4.29(ii) Complex Arguments

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5: Qiming Wang

… ►Web-based 3D graphics and visualization are her main research and development interests. … ►She is a developer of 2D and 3D graphics for the DLMF project.

6: Need Help?

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• How can I view ‘VRML’? What is it? See Viewing DLMF Interactive 3D Graphics.

• What do the colors mean? See About Color Map.

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7: 7.3 Graphics

§7.3 Graphics

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

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

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Figure 7.3.5: $|\mathrm{erf}\left(x+\mathrm{i}y\right)|$, $-3\le x\le 3$, $-3\le y\le 3$. … Magnify 3D Help

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Figure 7.3.6: $|\mathrm{erfc}\left(x+\mathrm{i}y\right)|$, $-3\le x\le 3$, $-3\le y\le 3$. … Magnify 3D Help

8: 4.3 Graphics

§4.3 Graphics

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Figure 4.3.1: $\ln x$ and ${\mathrm{e}}^x$. … Magnify

… ►In the graphics shown in this subsection height corresponds to the absolute value of the function and color to the phase. … ►

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Figure 4.3.3: $\ln \left(x+\mathrm{i}y\right)$ (principal value). … Magnify 3D Help

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Figure 4.3.4: ${\mathrm{e}}^{x+\mathrm{i}y}$. Magnify 3D Help

9: 11.3 Graphics

§11.3 Graphics

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Figure 11.3.1: ${𝐇}_{\nu }\left(x\right)$ for $0\le x\le 12$ and $\nu =0,\frac{1}{2},1,\frac{3}{2},2,3$. Magnify

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Figure 11.3.2: ${𝐊}_{\nu }\left(x\right)$ for and $\nu =0,\frac{1}{2},1,\frac{3}{2},2,3$. Magnify

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Figure 11.3.3: ${𝐇}_{\nu }\left(x\right)$ for $0\le x\le 12$ and $\nu =-3,-2,-\frac{3}{2},-1,-\frac{1}{2}$. Magnify

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Figure 11.3.4: ${𝐊}_{\nu }\left(x\right)$ for and $\nu =-4,-3,-2,-1,0$. … Magnify

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10: Viewing DLMF Interactive 3D Graphics

Viewing DLMF Interactive 3D Graphics

… ►WebGL is a JavaScript API (application programming interface) for rendering 3D graphics in a web browser without the use of a plugin. Our WebGL code is based on the X3DOM framework which allows the building of the WebGL application around X3D, an XML based graphics code. … ►” VRML (Virtual Reality Modeling Language) is a standard file format for viewing 3D graphics on the web and X3D is its successor. …