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21: 4.42 Solution of Triangles

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4.42.7 $$\text{<span class="ltx\_text hilite">area</span>}=\frac{1}{2}bc\sin A={\left(s(s-a)(s-b)(s-c)\right)}^{1/2},$$

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Symbols:

$\sin z$: sine function, $a$: length, $b$: base, $c$: length, $s$: semi-perimeter and $A$: angle

A&S Ref:

4.3.148

Permalink:

http://dlmf.nist.gov/4.42.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §4.42(ii), §4.42 and Ch.4

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22: 21.9 Integrable Equations

… ►Riemann theta functions arise in the study of integrable differential equations that have applications in many areas, including fluid mechanics (Ablowitz and Segur (1981, Chapter 4)), magnetic monopoles (Ercolani and Sinha (1989)), and string theory (Deligne et al. (1999, Part 3)). …

23: Software Index

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An increasing number of published books have included digital media containing software described in the book. Often, the collection of software covers a fairly broad area. Such software is typically developed by the book author. While it is not professionally packaged, it often provides a useful tool for readers to experiment with the concepts discussed in the book. The software itself is typically not formally supported by its authors.

… ►The following are web-based software repositories with significant holdings in the area of special functions. …

24: 28.33 Physical Applications

… ►We shall derive solutions to the uniform, homogeneous, loss-free, and stretched elliptical ring membrane with mass $\rho$ per unit area, and radial tension $\tau$ per unit arc length. …

25: Mathematical Introduction

… ►As a consequence, in addition to providing more information about the special functions that were covered in AMS 55, the NIST Handbook includes several special functions that have appeared in the interim in applied mathematics, the physical sciences, and engineering, as well as in other areas. …

26: 18.40 Methods of Computation

… ►The problem of moments is simply stated and the early work of Stieltjes, Markov, and Chebyshev on this problem was the origin of the understanding of the importance of both continued fractions and OP’s in many areas of analysis. …

27: 10.22 Integrals

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$A=s(s-a)(s-b)(s-c),$

… ►(Thus if $a,b,c$ are the sides of a triangle, then $A^{\frac{1}{2}}$ is the area of the triangle.) … ►

10.22.74

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Symbols:

$J_{\nu }\left(z\right)$: Bessel function of the first kind, $\mathrm{\Gamma }\left(z\right)$: gamma function, $\pi$: the ratio of the circumference of a circle to its diameter, $dx$: differential of $x$ , $\int$: integral, $\nu$: complex parameter and $A$: area

Keywords:

Mellin transform

Referenced by:

§10.22(iv), §10.22(iv)

Permalink:

http://dlmf.nist.gov/10.22.E74

Encodings:

pMML, png, TeX

See also:

Annotations for §10.22(iv), §10.22(iv), §10.22 and Ch.10

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10.22.75

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Symbols:

$J_{\nu }\left(z\right)$: Bessel function of the first kind, $Y_{\nu }\left(z\right)$: Bessel function of the second kind, $\mathrm{\Gamma }\left(z\right)$: gamma function, $\pi$: the ratio of the circumference of a circle to its diameter, $dx$: differential of $x$ , $\int$: integral, $\nu$: complex parameter and $A$: area

Keywords:

Mellin transform

Referenced by:

§10.22(iv), §10.22(iv)

Permalink:

http://dlmf.nist.gov/10.22.E75

Encodings:

pMML, png, TeX

See also:

Annotations for §10.22(iv), §10.22(iv), §10.22 and Ch.10

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28: Bibliography

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Algorithm 39: Areas under the normal curve. The Computer Journal 12 (2), pp. 197–198.

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Notes:

Includes Algol program, maximum accuracy 12D.

External Links:

Document

Referenced by:

§7.25(ii).

Encodings:

BibTeX

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29: Bibliography M

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Table of the ratio: Area to bounding ordinate, for any portion of normal curve. Biometrika 18, pp. 395–400.

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External Links:

FullText, ZentralBlatt

Referenced by:

§7.8.

Encodings:

BibTeX

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30: 1.5 Calculus of Two or More Variables

… ►where $D$ is the image of $D^{\ast }$ under a mapping $(u,v)\to (x(u,v),y(u,v))$ which is one-to-one except perhaps for a set of points of area zero. …