… ► 254, American Mathematical Society, 2000; Special Functions—Proceedings of the International Workshop, Hong Kong, June 21–25, 1999, World Scientific, 2000; Special Functions 2000: Current Perspective and Future Directions (with J. …

8: 26.3 Lattice Paths: Binomial Coefficients

… ►

Table 26.3.1: Binomial coefficients

\genfrac{(}{)}{0.0pt}{}{m}{n}

► ►►►

$m$	$n$
$m$	…
7	1	7	21	35	35	21	7	1
…

► ►

Table 26.3.2: Binomial coefficients

\genfrac{(}{)}{0.0pt}{}{m+n}{m}

for lattice paths.

► ►►►►

$m$	$n$
$m$	…
2	1	3	6	10	15	21	28	36	45
…
5	1	6	21	56	126	252	462	792	1287
…

► …

9: Staff

… ►

Bernard Deconinck, University of Washington, Chap. 21

… ►

Bernard Deconinck, University of Washington, for Chaps. 19, 21

…

10: 1.3 Determinants, Linear Operators, and Spectral Expansions

… ►

1.3.1

\det[a_{jk}]=\begin{vmatrix}a_{11}&a_{12}\\ a_{21}&a_{22}\end{vmatrix}=a_{11}a_{22}-a_{12}a_{21}.

ⓘ

Symbols:: $\det$ : determinant, $j$ : integer and $k$ : integer
Permalink:: http://dlmf.nist.gov/1.3.E1
Encodings:: pMML, png, TeX
See also:: Annotations for §1.3(i), §1.3(i), §1.3 and Ch.1

… ►

1.3.2

\det[a_{jk}]=\begin{vmatrix}a_{11}&a_{12}&a_{13}\\ a_{21}&a_{22}&a_{23}\\ a_{31}&a_{32}&a_{33}\end{vmatrix}=a_{11}\begin{vmatrix}a_{22}&a_{23}\\ a_{32}&a_{33}\end{vmatrix}-a_{12}\begin{vmatrix}a_{21}&a_{23}\\ a_{31}&a_{33}\end{vmatrix}+a_{13}\begin{vmatrix}a_{21}&a_{22}\\ a_{31}&a_{32}\end{vmatrix}=a_{11}a_{22}a_{33}-a_{11}a_{23}a_{32}-a_{12}a_{21}a% _{33}+a_{12}a_{23}a_{31}+a_{13}a_{21}a_{32}-a_{13}a_{22}a_{31}.

ⓘ

Symbols:: $\det$ : determinant, $j$ : integer and $k$ : integer
Permalink:: http://dlmf.nist.gov/1.3.E2
Encodings:: pMML, png, TeX
See also:: Annotations for §1.3(i), §1.3(i), §1.3 and Ch.1

… ►

1.3.8

{\begin{vmatrix}a_{11}&a_{12}\\ a_{21}&a_{22}\end{vmatrix}}^{2}\leq(a^{2}_{11}+a^{2}_{12})(a^{2}_{21}+a^{2}_{2% 2}),

ⓘ

Symbols:: $\det$ : determinant
Permalink:: http://dlmf.nist.gov/1.3.E8
Encodings:: pMML, png, TeX
See also:: Annotations for §1.3(i), §1.3(i), §1.3 and Ch.1

…

现场21点游戏大厅【打开网址∶3344yule.com】网上现场21点游戏规则,真人棋牌游戏平台【官网地址：3344yule.com】正规博彩平台

1—10 of 70 matching pages

1: 21 Multidimensional Theta Functions

Chapter 21 Multidimensional Theta Functions

2: 34.6 Definition: $\mathit{9j}$ Symbol

3: 30 Spheroidal Wave Functions

4: 34.7 Basic Properties: $\mathit{9j}$ Symbol

5: Bernard Deconinck

6: 34.14 Tables

7: Mourad E. H. Ismail

8: 26.3 Lattice Paths: Binomial Coefficients

9: Staff

10: 1.3 Determinants, Linear Operators, and Spectral Expansions

现场21点游戏大厅【打开网址∶3344yule.com】网上现场21点游戏规则,真人棋牌游戏平台【官网地址：3344yule.com】正规博彩平台

1—10 of 70 matching pages

1: 21 Multidimensional Theta Functions

Chapter 21 Multidimensional Theta Functions

2: 34.6 Definition: 9 ⁢ j Symbol

3: 30 Spheroidal Wave Functions

4: 34.7 Basic Properties: 9 ⁢ j Symbol

5: Bernard Deconinck

6: 34.14 Tables

7: Mourad E. H. Ismail

8: 26.3 Lattice Paths: Binomial Coefficients

9: Staff

10: 1.3 Determinants, Linear Operators, and Spectral Expansions

2: 34.6 Definition: $\mathit{9j}$ Symbol

4: 34.7 Basic Properties: $\mathit{9j}$ Symbol