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21: 15.3 Graphics

§15.3 Graphics

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§15.3(i) Graphs

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Figure 15.3.7: $|𝐅(-3,\frac{3}{5};u+\mathrm{i}v;\frac{1}{2})|,-6\le u\le 2,-2\le v\le 2$. Magnify 3D Help

22: Browsers

… ►Although we are not yet encoding our graphics in SVG, will be looking to make that conversion in the future. …

23: 27.17 Other Applications

… ►Schroeder (2006) describes many of these applications, including the design of concert hall ceilings to scatter sound into broad lateral patterns for improved acoustic quality, precise measurements of delays of radar echoes from Venus and Mercury to confirm one of the relativistic effects predicted by Einstein’s theory of general relativity, and the use of primes in creating artistic graphical designs.

24: Preface

… ►All of the mathematical information contained in the Handbook is also contained in the DLMF, along with additional features such as more graphics, expanded tables, and higher members of some families of formulas; in consequence, in the Handbook there are occasional gaps in the numbering sequences of equations, tables, and figures. … ►Among these capabilities are: a facility to allow users to download LaTeX and MathML encodings of every formula into document processors and software packages (eventually, a fully semantic downloading capability may be possible); a search engine that allows users to locate formulas based on queries expressed in mathematical notation; and user-manipulable 3-dimensional color graphics. … ►Saunders was responsible for mesh generation for curves and surfaces, data computation and validation, graphics production, and interactive Web visualization. … Conlon (bibliography), Gloria Wiersma (LaTeX), Qiming Wang (graphics generation, graphics viewers), and Brian Antonishek (graphics viewers). …

25: 18.4 Graphics

§18.4 Graphics

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Figure 18.4.5: Laguerre polynomials $L_n\left(x\right)$, $n=1,2,3,4,5$. Magnify

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Figure 18.4.6: Laguerre polynomials $L_3^{(\alpha )}\left(x\right)$, $\alpha =0,1,2,3,4$. Magnify

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26: 8.3 Graphics

§8.3 Graphics

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§8.3(i) Real Variables

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Figure 8.3.7: $x^{-a}-{\gamma }^{\ast }(a,x)$ (= $x^{-a}Q(a,x)$), $0\le x\le 4$, $-5\le a\le 5$. Magnify 3D Help

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§8.3(ii) Complex Argument

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

27: 20.3 Graphics

§20.3 Graphics

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§20.3(i) $\theta$-Functions: Real Variable and Real Nome

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§20.3(ii) $\theta$-Functions: Complex Variable and Real Nome

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

28: Bonita V. Saunders

… ►As the principal developer of graphics for the DLMF, she has collaborated with other NIST mathematicians, computer scientists, and student interns to produce informative graphs and dynamic interactive visualizations of elementary and higher mathematical functions over both simply and multiply connected domains. …

29: Philip J. Davis

… ►After receiving an overview of the project and watching a short demo that included a few preliminary colorful, but static, 3D graphs constructed for the first Chapter, “Airy and Related Functions”, written by Olver, Davis expressed the hope that designing a web-based resource would allow the team to incorporate interesting computer graphics, such as function surfaces that could be rotated and examined. This immediately led to discussions among some of the project members about what might be possible, and the discovery that some interactive graphics work had already been done for the NIST Matrix Market, a publicly available repository of test matrices for comparing the effectiveness of numerical linear algebra algorithms. ►Davis’s comments about our uninspired graphs sparked the research and design of techniques for creating interactive 3D visualizations of function surfaces, which grew in sophistication as our knowledge and the technology for developing 3D graphics on the web advanced over the years. …

30: 23.4 Graphics

§23.4 Graphics

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§23.4(i) Real Variables

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Figure 23.4.7: $\mathrm{\wp }\left(x\right)$ with ${\omega }_1=K\left(k\right)$, ${\omega }_3=\mathrm{i}{K}^{\prime }\left(k\right)$ for $0\le x\le 9$, $k^2$ = 0. … Magnify

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§23.4(ii) Complex Variables

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Figure 23.4.12: $\mathrm{\wp }(3.7;a+\mathrm{i}b,0)$ for $-5\le a\le 3$, $-4\le b\le 4$. … Magnify 3D Help