.币安法国球队网址『世界杯佣金分红55%，咨询专员：@ky975』.uiq.k2q1w9-2022年11月29日1时52分6秒maooc00kk

(0.003 seconds)

31—40 of 305 matching pages

31: 24.13 Integrals

… ►For other integrals see Prudnikov et al. (1990, pp. 55–57).

B. V. Saunders and Q. Wang (2000) From 2D to 3D: Numerical Grid Generation and the Visualization of Complex Surfaces, Proceedings of the 7th International Conference on Numerical Grid Generation in Computational Field Simulations, Whistler, British Columbia, Canada, September 25-28, 2000.

… ►

B. V. Saunders and Q. Wang (2005) Boundary/Contour Fitted Grid Generation for Effective Visualizations in a Digital Library of Mathematical Functions, Proceedings of the 9th International Conference on Numerical Grid Generation in Computational Field Simulations, San Jose, June 11–18, 2005. pp. 61–71.

►

Q. Wang and B. V. Saunders (2005) Web-Based 3D Visualization in a Digital Library of Mathematical Functions, Proceedings of the Web3D Symposium, Bangor, UK, March 29–April 1, 2005.

►

B. V. Saunders and Q. Wang (2006) From B-Spline Mesh Generation to Effective Visualizations for the NIST Digital Library of Mathematical Functions, in Curve and Surface Design, Proceedings of the Sixth International Conference on Curves and Surfaces, Avignon, France June 29–July 5, 2006, pp. 235–243.

… ►

Q. Wang, B. V. Saunders and S. Ressler (2007) Dissemination of 3D Visualizations of Complex Function Data for the NIST Digital Library of Mathematical Functions, CODATA Data Science Journal 6 (2007), pp. S146–S154.

…

33: Staff

… ►

Richard B. Paris, University of Abertay, Chaps. 8, 11

… ►

Nico M. Temme, Centrum Wiskunde Informatica, Chaps. 3, 6, 7, 12

… ►

Hans Volkmer, University of Wisconsin, Milwaukee, Chaps. 29, 30

… ►

Richard B. Paris, University of Abertay Dundee, for Chaps. 8, 11 (deceased)

… ►

Hans Volkmer, University of Wisconsin–Milwaukee, for Chaps. 29, 30

…

34: 34.6 Definition: $\mathit{9j}$ Symbol

… ►The

\mathit{9j}

symbol may be defined either in terms of

\mathit{3j}

symbols or equivalently in terms of

\mathit{6j}

symbols: ►

34.6.1

\begin{Bmatrix}j_{11}&j_{12}&j_{13}\\ j_{21}&j_{22}&j_{23}\\ j_{31}&j_{32}&j_{33}\end{Bmatrix}=\sum_{\mbox{\scriptsize all }m_{rs}}\begin{% pmatrix}j_{11}&j_{12}&j_{13}\\ m_{11}&m_{12}&m_{13}\end{pmatrix}\begin{pmatrix}j_{21}&j_{22}&j_{23}\\ m_{21}&m_{22}&m_{23}\end{pmatrix}\begin{pmatrix}j_{31}&j_{32}&j_{33}\\ m_{31}&m_{32}&m_{33}\end{pmatrix}\*\begin{pmatrix}j_{11}&j_{21}&j_{31}\\ m_{11}&m_{21}&m_{31}\end{pmatrix}\begin{pmatrix}j_{12}&j_{22}&j_{32}\\ m_{12}&m_{22}&m_{32}\end{pmatrix}\begin{pmatrix}j_{13}&j_{23}&j_{33}\\ m_{13}&m_{23}&m_{33}\end{pmatrix},

ⓘ

Defines:: $\begin{Bmatrix}\NVar{j_{11}}&\NVar{j_{12}}&\NVar{j_{13}}\\ \NVar{j_{21}}&\NVar{j_{22}}&\NVar{j_{23}}\\ \NVar{j_{31}}&\NVar{j_{32}}&\NVar{j_{33}}\end{Bmatrix}$ : $\mathit{9j}$ symbol
Symbols:: $\begin{pmatrix}\NVar{j_{1}}&\NVar{j_{2}}&\NVar{j_{3}}\\ \NVar{m_{1}}&\NVar{m_{2}}&\NVar{m_{3}}\end{pmatrix}$ : $\mathit{3j}$ symbol, $j,j_{r}$ : non-negative integers or non-negative integers plus one half., $r$ : nonnegative integer and $s$ : integer
Permalink:: http://dlmf.nist.gov/34.6.E1
Encodings:: pMML, png, TeX
See also:: Annotations for §34.6 and Ch.34

►

34.6.2

\begin{Bmatrix}j_{11}&j_{12}&j_{13}\\ j_{21}&j_{22}&j_{23}\\ j_{31}&j_{32}&j_{33}\end{Bmatrix}=\sum_{j}(-1)^{2j}(2j+1)\begin{Bmatrix}j_{11}% &j_{21}&j_{31}\\ j_{32}&j_{33}&j\end{Bmatrix}\begin{Bmatrix}j_{12}&j_{22}&j_{32}\\ j_{21}&j&j_{23}\end{Bmatrix}\begin{Bmatrix}j_{13}&j_{23}&j_{33}\\ j&j_{11}&j_{12}\end{Bmatrix}.

ⓘ

Symbols:: $\begin{Bmatrix}\NVar{j_{11}}&\NVar{j_{12}}&\NVar{j_{13}}\\ \NVar{j_{21}}&\NVar{j_{22}}&\NVar{j_{23}}\\ \NVar{j_{31}}&\NVar{j_{32}}&\NVar{j_{33}}\end{Bmatrix}$ : $\mathit{9j}$ symbol, $\begin{Bmatrix}\NVar{j_{1}}&\NVar{j_{2}}&\NVar{j_{3}}\\ \NVar{l_{1}}&\NVar{l_{2}}&\NVar{l_{3}}\end{Bmatrix}$ : $\mathit{6j}$ symbol and $j,j_{r}$ : non-negative integers or non-negative integers plus one half.
Referenced by:: §34.13
Permalink:: http://dlmf.nist.gov/34.6.E2
Encodings:: pMML, png, TeX
See also:: Annotations for §34.6 and Ch.34

…

35: 8.2 Definitions and Basic Properties

… ►

8.2.11

\Gamma\left(a,ze^{\pm\pi i}\right)=\Gamma\left(a\right)(1-z^{a}e^{\pm\pi ia}% \gamma^{*}\left(a,-z\right)).

ⓘ

Symbols:: $\Gamma\left(\NVar{z}\right)$ : gamma function, $\pi$ : the ratio of the circumference of a circle to its diameter, $\mathrm{e}$ : base of natural logarithm, $\mathrm{i}$ : imaginary unit, $\Gamma\left(\NVar{a},\NVar{z}\right)$ : incomplete gamma function, $\gamma^{*}\left(\NVar{a},\NVar{z}\right)$ : incomplete gamma function, $z$ : complex variable and $a$ : parameter
Permalink:: http://dlmf.nist.gov/8.2.E11
Encodings:: pMML, png, TeX
See also:: Annotations for §8.2(ii), §8.2 and Ch.8

…

36: 26.2 Basic Definitions

… ►If, for example, a permutation of the integers 1 through 6 is denoted by

256413

, then the cycles are

{\left(1,2,5\right)}

{\left(3,6\right)}

, and

{\left(4\right)}

. …The function

\sigma

also interchanges 3 and 6, and sends 4 to itself. … ►As an example,

\{1,3,4\}

\{2,6\}

\{5\}

is a partition of

\{1,2,3,4,5,6\}

. … ►

Table 26.2.1: Partitions

p\left(n\right)

► ►►►►

$n$	$p\left(n\right)$	$n$	$p\left(n\right)$	$n$	$p\left(n\right)$
…
6	11	23	1255	40	37338
…
11	56	28	3718	45	89134
…

►

37: 26.9 Integer Partitions: Restricted Number and Part Size

… ►

Table 26.9.1: Partitions

p_{k}\left(n\right)

► ►►►►►

$n$	$k$
$n$	…
6	0	1	4	7	9	10	11	11	11	11	11
7	0	1	4	8	11	13	14	15	15	15	15
…
9	0	1	5	12	18	23	26	28	29	30	30
…

► … ►The conjugate to the example in Figure 26.9.1 is

6+5+4+2+1+1+1

. … ►

p_{3}\left(n\right)=1+\left\lfloor\frac{n^{2}+6n}{12}\right\rfloor.

…

38: 4.17 Special Values and Limits

… ►

Table 4.17.1: Trigonometric functions: values at multiples of

\frac{1}{12}\pi

► ►►►►►

$\theta$	$\sin\theta$	$\cos\theta$	$\tan\theta$	$\csc\theta$	$\sec\theta$	$\cot\theta$
…
$\pi/6$	$\frac{1}{2}$	$\frac{1}{2}\sqrt{3}$	$\frac{1}{3}\sqrt{3}$	$2$	$\frac{2}{3}\sqrt{3}$	$\sqrt{3}$
…
$5\pi/6$	$\frac{1}{2}$	$-\frac{1}{2}\sqrt{3}$	$-\frac{1}{3}\sqrt{3}$	$2$	$-\frac{2}{3}\sqrt{3}$	$-\sqrt{3}$
$11\pi/12$	$\frac{1}{4}\sqrt{2}(\sqrt{3}-1)$	$-\frac{1}{4}\sqrt{2}(\sqrt{3}+1)$	$-(2-\sqrt{3})$	$\sqrt{2}(\sqrt{3}+1)$	$-\sqrt{2}(\sqrt{3}-1)$	$-(2+\sqrt{3})$
…