graphical interpretation via Glaisher notation

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1: 22.4 Periods, Poles, and Zeros

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§22.4(ii) Graphical Interpretation via Glaisher’s Notation

… ►Using the p,q notation of (22.2.10), Figure 22.4.2 serves as a mnemonic for the poles, zeros, periods, and half-periods of the 12 Jacobian elliptic functions as follows. …

2: 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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• How do I search within DLMF? See Guide to Searching the DLMF.

• See also the Index or Notations sections.

• Links to definitions, keywords, annotations and other interesting information can be found in the Info boxes by clicking or hovering the mouse over the icon next to each formula, table, figure, and section heading.

3: 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).

4: 28.16 Asymptotic Expansions for Large $q$

… ►For graphical interpretation, see Figures 28.13.1 and 28.13.2. …

5: 10.3 Graphics

§10.3 Graphics

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§10.3(i) Real Order and Variable

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§10.3(ii) Real Order, Complex Variable

►In the graphics shown in this subsection, height corresponds to the absolute value of the function and color to the phase. … ►For the notation see §10.24. …

6: 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

7: 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

8: Preface

… ►Olver was responsible for organizing and editing the mathematical content after receiving it from the authors; for communicating with the associate editors, authors, validators, and other technical experts; and for assembling the Notations section and the Index. … ►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). …

9: 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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10: 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.