area of triangle

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11: Alexander A. Its

… ►Current research areas of Its are mathematical physics, special functions, and integrable systems. …

12: Stephen M. Watt

… ►His areas of research include algorithms and systems for computer algebra, programming languages and compilers, mathematical handwriting recognition and mathematical document analysis. …

13: 27.17 Other Applications

… ►There are also applications of number theory in many diverse areas, including physics, biology, chemistry, communications, and art. …

14: Annie A. M. Cuyt

… ►Her main research interest is in the area of numerical approximation theory and its applications to a diversity of problems in scientific computing. …

15: 10.22 Integrals

… ►

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

\int_{0}^{\infty}J_{\nu}\left(at\right)J_{\nu}\left(bt\right)J_{\nu}\left(ct% \right)t^{1-\nu}\,\mathrm{d}t=\begin{cases}\dfrac{2^{\nu-1}A^{\nu-\frac{1}{2}}% }{\pi^{\frac{1}{2}}(abc)^{\nu}\Gamma\left(\nu+\frac{1}{2}\right)},&A>0,\\ 0,&A\leq 0.\end{cases}

ⓘ

Symbols:: $J_{\NVar{\nu}}\left(\NVar{z}\right)$ : Bessel function of the first kind, $\Gamma\left(\NVar{z}\right)$ : gamma function, $\pi$ : the ratio of the circumference of a circle to its diameter, $\,\mathrm{d}\NVar{x}$ : 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

… ►

10.22.75

\int_{0}^{\infty}Y_{\nu}\left(at\right)J_{\nu}\left(bt\right)J_{\nu}\left(ct% \right)t^{1+\nu}\,\mathrm{d}t=\begin{cases}-\dfrac{(abc)^{\nu}(-A)^{-\nu-\frac% {1}{2}}}{\pi^{\frac{1}{2}}2^{\nu+1}\Gamma\left(\frac{1}{2}-\nu\right)},&0<a<|b% -c|,\\ 0,&|b-c|<a<b+c,\\ \dfrac{(abc)^{\nu}(-A)^{-\nu-\frac{1}{2}}}{\pi^{\frac{1}{2}}2^{\nu+1}\Gamma% \left(\frac{1}{2}-\nu\right)},&a>b+c.\end{cases}

ⓘ

Symbols:: $J_{\NVar{\nu}}\left(\NVar{z}\right)$ : Bessel function of the first kind, $Y_{\NVar{\nu}}\left(\NVar{z}\right)$ : Bessel function of the second kind, $\Gamma\left(\NVar{z}\right)$ : gamma function, $\pi$ : the ratio of the circumference of a circle to its diameter, $\,\mathrm{d}\NVar{x}$ : 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

…

16: 19.33 Triaxial Ellipsoids

… ►

§19.33(i) Surface Area

►The surface area of an ellipsoid with semiaxes

a, b, c

, and volume

V=4\pi abc/3

is given by ►

19.33.1

S=3VR_{G}\left(a^{-2},b^{-2},c^{-2}\right),

ⓘ

Symbols:: $R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)$ : symmetric elliptic integral of second kind, $V$ : volume and $S$ : area
Referenced by:: §19.33(i)
Permalink:: http://dlmf.nist.gov/19.33.E1
Encodings:: pMML, png, TeX
See also:: Annotations for §19.33(i), §19.33 and Ch.19

… ►

19.33.2

\frac{S}{2\pi}=c^{2}+\frac{ab}{\sin\phi}\left(E\left(\phi,k\right){\sin}^{2}% \phi+F\left(\phi,k\right){\cos}^{2}\phi\right),

a\geq b\geq c

ⓘ

Symbols:: $\pi$ : the ratio of the circumference of a circle to its diameter, $\cos\NVar{z}$ : cosine function, $F\left(\NVar{\phi},\NVar{k}\right)$ : Legendre’s incomplete elliptic integral of the first kind, $E\left(\NVar{\phi},\NVar{k}\right)$ : Legendre’s incomplete elliptic integral of the second kind, $\sin\NVar{z}$ : sine function, $\phi$ : real or complex argument, $k$ : real or complex modulus and $S$ : area
Permalink:: http://dlmf.nist.gov/19.33.E2
Encodings:: pMML, png, TeX
See also:: Annotations for §19.33(i), §19.33 and Ch.19

…

17: Richard A. Askey

… ►Over his career his primary research areas were in Special Functions and Orthogonal Polynomials, but also included other topics from Classical Analysis and related areas. …

18: 34.2 Definition: $\mathit{3j}$ Symbol

… ►They must form the sides of a triangle (possibly degenerate). They therefore satisfy the triangle conditions …

19: 32.16 Physical Applications

… ►Statistical physics, especially classical and quantum spin models, has proved to be a major area for research problems in the modern theory of Painlevé transcendents. …

… ►Olkin’s research covered a broad range of areas, including multivariate analysis, reliability theory, matrix theory, statistical models in the social and behavioral sciences, life distributions, and meta-analysis. …