\a!&=\a_1!\cdots\a_n!\qquad\text{(as usual, }0!=1!=1),
...a}{\b}=\binom{\a_1}{\b_1}\cdots\binom{\a_n}{\b_n}=\frac{\a!}{\b!(\a-\b)!},\qquad \text{if}\quad \a\geqslant\b.
3 KB (512 words) - 06:16, 13 June 2022
i^{p+1} H^{(1)}_p (ix) \qquad \mbox{and} \qquad i^{-(p+1)} H^{(2)}_p (-ix)
2 KB (376 words) - 16:10, 2 April 2014
L (f) = \int_X f\, d\mu \qquad \forall f\in C (X)\, .
L (f) = \int_X fg\, d\mu\qquad \forall f\in C(X)\, .
3 KB (451 words) - 17:37, 18 August 2012
...\gamma^{\beta} \gamma^{\alpha} = - 2 \eta^{\alpha \beta} \mathsf{I}_{4}, \qquad \forall \alpha,\beta \in \{ 0,1,2,3 \}.
..._{2} & \mathbf{0}_{2} \\ \mathbf{0}_{2} & - \mathsf{I}_{2} \end{bmatrix}; \qquad
2 KB (328 words) - 16:06, 15 December 2016
\[\delta(-x)=\delta(x);\qquad\delta(cx)=|c|^{-1}\delta(x),\quad c=\mathrm{const},\]
\[x\delta(x)=0;\qquad\delta(x)+x\delta'(x)=0,\]
2 KB (390 words) - 22:12, 31 December 2018
$$|\{f,z\}|\leq\frac6{{(1-|z|^2)}^2},\qquad|z|<1.$$
$$|\{f,z\}|\leq\frac2{{(1-|z|^2)}^2},\qquad|z|<1,$$
3 KB (443 words) - 11:10, 30 December 2018
\left<\cdot,\cdot\right>:\Gamma(E)\times\Gamma(E^*)\to C^\infty(B),\qquad (s,s^*)\mapsto \left< s,s^*\right>(b)=\left< s(b),s^*(b)\right>.
585 bytes (112 words) - 13:20, 20 May 2012
$$\cos x=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\dotsb,\qquad-\infty<x<\infty.$$
2 KB (283 words) - 12:43, 14 February 2020
\forall A \subseteq \mathfrak{P}: \qquad
960 bytes (147 words) - 04:53, 24 April 2017
$$\Spin_3\simeq \def\SL{ {\rm SL}}\SL_2,\qquad \Spin_2 \simeq \SL_2\times \SL_2,$$
$$\Spin_5 \simeq \def\Sp{ {\rm Sp}}\Sp_4,\qquad \Spin_6 \simeq \SL_4.$$
4 KB (648 words) - 13:16, 7 April 2023
\int_\Gamma f(z)\, dz = 0\, \qquad\qquad \mbox{for any}\, \Gamma \in \mathcal{P}\, ,
2 KB (358 words) - 17:23, 12 January 2014
\mu (D) = \inf\; \{ \mu (C): D\subset {\rm int}\, (C)\} \qquad \forall D\in \mathcal{C}\, .
\mu (D) = \inf\;\{\mu (C) : D\subset C \mbox{ and } C \mbox{ is open}\} \qquad \forall D\in \mathcal{C}
5 KB (751 words) - 09:47, 16 August 2013
g \circ f & = \mathsf{Id}_{X} \quad \text{on} ~ M, \qquad (1) \\
f \circ g & = \mathsf{Id}_{Y} \quad \text{on} ~ f[M], \qquad (2)
4 KB (752 words) - 03:29, 9 January 2017
{\rm ap}\,\limsup_{x\to x_0}\, f(x) \qquad \mbox{and}\qquad {\rm ap}\, \liminf_{x\to x_0}\, f(x)
...\downarrow 0} \frac{\lambda (G\cap ]x_0, x_0+r[)}{r} = 1 \qquad \mbox{and}\qquad \lim_{r\downarrow 0} \frac{\lambda (G\cap ]x_0-r, x_0[)}{r} = 1\,
5 KB (745 words) - 17:18, 18 August 2012
\mu (B)= \sup \{\mu(K): K\subset B, K \mbox{ compact}\} \qquad \forall B\in \mathcal{B}\,.
\mu (N) = \inf \{\mu (U): U\supset N,\, U \mbox{ open}\}\, \qquad \forall N\in \mathcal{B},
4 KB (498 words) - 22:40, 31 December 2017
H\circ i_A=i_B\circ h,\qquad i_A:A\to X,\ i_B:B\to Y.
X=\bigsqcup_x G(x),\quad Y=\bigsqcup_y G(y),\qquad G(x)=\{g\cdot x:~g\in G\},\quad G(y)=\{g\cdot y:~g\in G\}.
5 KB (894 words) - 09:02, 12 December 2013
...^q a_n b_n = \sum_{n=p}^{q-1} B_n (a_q - a_{n+1}) + B_q a_q - B_{p-1} a_p \qquad \forall 1\leq p < q\, .
860 bytes (157 words) - 20:29, 9 December 2013
\forall x \in \mathbb{R}: \qquad
\mathsf{P}(S_{n} = m) = \binom{n}{m} p^{m} (1 - p)^{n - m}, \qquad \text{where} ~ m \in \mathbb{Z} \cap [0,n],
5 KB (692 words) - 19:33, 7 July 2016
...mathrm{d}{s} \stackrel{\text{df}}{=} \int_{0}^{s} F(x(s)) ~ \mathrm{d}{s} \qquad (1)
\int_{\gamma} F(x) ~ \mathrm{d}{x_{k}}, \qquad k \in \{ 1,\ldots,n \}
9 KB (1,447 words) - 06:40, 1 December 2016
\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y} \qquad
\frac{\partial u}{\partial s} = \frac{\partial v}{\partial n} \qquad
7 KB (1,063 words) - 12:51, 22 March 2023