\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
{\rm dist}\, (x, Z_f)^\alpha \leq C |f(x)| \qquad \qquad \forall x \in K.
|f(x)-f(y)|^\theta \leq C |\nabla f (y)| \qquad \qquad \forall y\in V\, .
7 KB (1,088 words) - 21:21, 14 January 2021
f (x_0) \geq \limsup_{x\to x_0}\; f(x) \qquad \left(\mbox{resp. }\quad f(x_0)\leq \liminf_{x\to x_0}\; f(x)\right)\, .
F(x):= \inf_{f\in\mathcal{F}}\; f(x) \qquad \left(\mbox{resp.}\; \sup_{f\in\mathcal{F}}\; f(x)\right)
8 KB (1,260 words) - 15:29, 5 January 2017
\rd R\cdot v=KR,\qquad K=K(x,y)\in\R[x,y].
H(x,y)=R_1^{\lambda_1}(x,y)\cdots R_k^{\lambda_k}(x,y),\qquad \lambda_1,\dots,\lambda_k\in\C,
5 KB (809 words) - 09:08, 12 December 2013
K_n := c_n \frac{a_n}{a_{n+1}} - c_{n+1} \geq \delta \qquad \forall n\geq N\, ,
1,017 bytes (170 words) - 11:25, 10 December 2013
$$ D_t = (20n)^{n(n + 1)t/2}, \qquad b_t = nt + \left[{\frac{n(n + 1)}{4} + 1}\right], $$
2 KB (248 words) - 21:55, 14 January 2017
...\le t \le 1} |f(t) - S_n(t, f)| \le 12 \omega\left(\frac{1}{n}, f\right), \qquad n = 1, 2, \ldots.$$
$$\|f - S_n(f)\|_{L_p[0, 1]} \le 24 \omega_p \left(\frac{1}{n}, f\right), \qquad n = 1, 2, \ldots.$$
6 KB (1,003 words) - 05:01, 23 July 2018
1\qquad\text{if }t=s,\\
0\qquad\text{if }t\neq s.
3 KB (550 words) - 10:36, 23 May 2017
\mathsf{E} {F_{n}}(x) = F(x), \qquad
\forall z \in \mathbf{R}_{> 0}: \qquad
5 KB (778 words) - 04:08, 22 June 2017
b(u,v) = \overline{\langle Bu, v\rangle}, \qquad \forall u,v \in V, \\
b(B^{-1} l,v) = \overline{\langle l,v \rangle}, \qquad \forall v \in V, l\in V',
5 KB (784 words) - 03:17, 15 February 2024
...$ (\alpha + \beta) + \gamma = \alpha + (\beta + \gamma) \qquad \text{and} \qquad \alpha + 0 = \alpha = 0 + \alpha, $$ where $ 0 $ is the order type of the e
...gamma), \qquad \alpha \cdot 1 = \alpha = 1 \cdot \alpha \qquad \text{and} \qquad \alpha \cdot 0 = 0 = 0 \cdot \alpha, $$ where $ 1 $ is the order type of a
6 KB (1,008 words) - 17:31, 5 January 2017
D (\lambda f + \mu g) = \lambda Df + \mu Dg \qquad \forall \lambda, \mu \in \mathbb R, \forall f,g\in C^1 (M)\, ,
(f+g)' = f' + g' \qquad \mbox{and} \qquad (fg)' = fg' + gf'\, .
5 KB (757 words) - 10:34, 11 December 2013
\dot x=y,\quad \dot y=-x, \qquad (x,y)\in(\R^2,0),
\dot x=x+\cdots,\qquad \dot y=-y+\cdots,\qquad (x,y)\in(\C^2,0)
5 KB (706 words) - 09:05, 12 December 2013
D\in T_a M\iff D:C^\infty(M)\to\R,\qquad D(f\pm g)=Df\pm Dg,\ D(\lambda f)=\lambda Df,\ D(f\cdot g)=f(a)\cdot Dg+g(a
1 KB (196 words) - 08:55, 12 December 2013
f(z) = \sum_{k=-m}^\infty c_k (z-a)^k,\qquad a \neq \infty, c_{-m} \neq 0, z \in V,
f(z) = \sum_{k=-m}^\infty \frac{c_k}{z^k},\qquad a = \infty, c_{-m} \neq 0, z \in V',
3 KB (549 words) - 09:10, 18 January 2014
\frac{|a_{n+1}|}{|a_n|} \geq 1 - \frac{1}{n} \qquad \forall n \geq N\, ,
1 KB (228 words) - 10:49, 10 December 2013
...wnarrow 0} \frac{\lambda (B_r (x)\cap E)}{\omega_n r^n} \qquad \mbox{and} \qquad \liminf_{r\downarrow 0} \frac{\lambda (B_r (x)\cap E)}{\omega_n r^n}\, ,
\qquad \mbox{and}\qquad \theta^\alpha_* (\mu, x) =\liminf_{r\downarrow 0} \frac{\mu (B_r (x))}{\ome
10 KB (1,662 words) - 09:58, 16 August 2013
\sup\; \{\mu (C):C\subset E\mbox{ is closed}\} = \mu (E) \qquad \mbox{for any Borel set } E.
\sup\; \{\mu (C):C\subset E\mbox{ is compact}\} = \mu (E) \qquad \mbox{for any Borel set } E
5 KB (764 words) - 09:39, 16 August 2013
\mathbf{r} = \mathbf{r}(u,v) \qquad (1)
...hbf{r}}{\partial u},\frac{\partial \mathbf{r}}{\partial u} \right\rangle, \qquad
11 KB (1,911 words) - 18:57, 1 December 2016
...t(x^{k+1}, \dots, x^n \right) dx^\alpha dx^\beta,$$$$i,j = 1, \dots, k ; \qquad \alpha, \beta = k+1 , \dots , n.$$Otherwise the space is called irreducible
8 KB (1,254 words) - 14:07, 2 January 2014
f^{(\a)}=\p^\a f\in C^{m-|\a|}(U),\qquad 0\le |\a|\le m,\ f^{(0)}=f,
...\a(a,x)=f^\a(x)-\sum_{|\b|\le m-|\a|}\frac1{\b!}f^{\a+\b}(a)\cdot(x-a)^\b,\qquad x,a\in K,
5 KB (913 words) - 12:24, 12 December 2020
$$\dot z=A(t)z,\qquad z\in\CC^n,\quad t\in (\CC,t_*)\tag {LS}$$
...0(t)\partial^n+a_{n-1}(t)\partial^{n-1}+\cdots+a_{n-1}(t)\partial +a_n(t),\qquad \partial =\frac d{dt},\tag L
7 KB (1,237 words) - 11:48, 23 November 2023
$$f:K\times[0,1]\to Y, \qquad F_0:K=K\times\{0\}\to X$$
1 KB (187 words) - 22:36, 24 November 2013
...{\mu (B_r (x))} \int_{B_r (x)} |f(y)-f(x)|\, d\mu (y) = 0\qquad \mbox{and}\qquad \lim_{r\downarrow 0} \frac{\nu_s (B_r (x))}{\mu (B_r (x))}= 0\, .
4 KB (532 words) - 13:29, 30 November 2012
$$\beta(x_1, x_2) = b(x_1 \tensor x_2), \qquad x_1 \in V_1, \qquad x_2 \in V_2.$$
$$x_1, y \in V_1, \qquad x_2, z \in V_2, \qquad c \in A;$$
11 KB (1,992 words) - 03:52, 23 July 2018
S_n(f; x) = \frac1\pi \int_{-\pi}^\pi f(x+t) D_n() \, dt, \qquad n=0,1,\ldots,
(\vb{x}, \vb{y}) = x_1y_1 + \cdots + x_N y_N, \qquad |\vb{x}| = \sqrt{(\vb{x}, \vb{x})}.
6 KB (1,047 words) - 11:37, 13 February 2024
F (t) := \frac{1}{t} \int_0^t \left(f(x+u)+f(x-u) - 2 f(x)\right)\, du \qquad \mbox{for } t>0
1 KB (216 words) - 20:45, 16 October 2012
\bigcup_{i=1}^\infty A_i \in \mathcal{A} \qquad \mbox{whenever } \{A_i\}_{i\in \mathbb N}\subset \mathcal{A}\, .
2 KB (231 words) - 09:47, 16 August 2013
\frac{x^2}{p}-\frac{y^2}{q}=2z, \qquad\text{where}\;p,q>0.
2 KB (252 words) - 11:12, 25 May 2016
\qquad \forall x\in E\, .
\qquad \forall x\in E\, .
6 KB (865 words) - 22:40, 17 August 2013
$$x=\frac{2at^2}{t^2+1},\qquad y=\frac{2at^3}{t^2+1}.$$
2 KB (300 words) - 09:39, 26 March 2023
|f(x)-f(y)|\leq C|x-y|\qquad \mbox{for every } x,y\in U\, .
2 KB (249 words) - 14:09, 2 May 2014
$$\sin x=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\dotsb,\qquad-\infty<x<\infty.$$
3 KB (441 words) - 13:51, 14 February 2020
F'. H = F_n, \qquad G'. H = G_n,
2 KB (288 words) - 04:27, 15 February 2024
\forall i \in J, ~ \forall \mu_{i} \in M_{i}: \qquad
2 KB (296 words) - 06:03, 8 April 2023
...^{\eta_{1}} \cdot \beta_{1} + \cdots + \gamma^{\eta_{n}} \cdot \beta_{n}, \qquad (1) \\
\eta > \eta_{1} > \ldots > \eta_{n}, \qquad 0 \leq \beta_{i} < \gamma, \qquad (2)
9 KB (1,404 words) - 18:33, 4 December 2017
\partial x_n^{\alpha_n}},\qquad D^{0}f=f,
\qquad (1\leq p< \infty).
8 KB (1,334 words) - 17:47, 30 November 2012
\forall f \in C(X): \qquad
\forall f \in {C_{0}}(X): \qquad
5 KB (819 words) - 17:08, 6 January 2017
f(z) = \frac{p(z)}{q(z)} \qquad \mbox{for every}\qquad z\in U\cap C\, .
5 KB (819 words) - 10:11, 18 January 2014
A, ~ 2^{A}, ~ 2^{2^{A}}, ~ 2^{2^{2^{A}}}, ~ \ldots \qquad (1)
\sum_{t \in T} \alpha_{t} < \prod_{t \in T} \beta_{t}. \qquad (2)
9 KB (1,402 words) - 11:57, 10 April 2018
A^{*} = A, \qquad
B^{*} B = A - A^{2} + c \mathbf{1}, \qquad
5 KB (814 words) - 07:12, 24 January 2024
n _ {j}\qquad \textrm{ if }i \neq j ,\qquad\qquad \atop n _ {j} - 1 \ \ \textrm{ if } \ i = j,\ i,\ j = 1 \dots m,}
9 KB (1,344 words) - 16:08, 6 February 2020
F(x) = G(x,F \uparrow x), \qquad (\star)
2 KB (351 words) - 21:15, 29 January 2017
f(x) = l(x),\qquad f(y) \ge l(y),\qquad y \in G. \tag{4}
...m\limits_{i = 1}^{n} \frac{\partial f(x)}{\partial x^i} (y^i - x^i) \ge 0,\qquad x, y \in G.
9 KB (1,555 words) - 08:20, 25 July 2013
f^{\pm} (x_1, \ldots, x_n) \leq f^{\pm} (y_1, \ldots, y_n) \qquad \mbox{if } x_i\leq y_i \, \forall i\, .
2 KB (323 words) - 09:38, 16 August 2013
|f(x)-f(x')| \leq M|x-x'|\qquad \forall x,x'\in [a,b]\, .
|f(x)-f(x')|\leq M |x-x'|^\alpha \qquad \forall x,x'\in \mathbb R
5 KB (736 words) - 09:19, 17 June 2014
\left|\int_A f (x) \rd\lambda (x)\right| < \varepsilon \qquad \mbox{for every measurable set}\, A \mbox{ with } \lambda (A)< \delta\, .
\nu (A) = \int_A f\, \rd\mu \qquad \text{for every } A\in\mathcal{B}.
9 KB (1,407 words) - 11:50, 4 February 2021
Y_\nu (z) = \frac{J_\nu (z) \cos \nu \pi - J_{-\nu} (z)}{\sin \nu \pi} \qquad \mbox{for}\; \nu\not\in \mathbb Z
Y_n (z) = \lim_{\nu\to n} Y_\nu (z) \qquad \mbox{for}\; n\in \mathbb Z\,
22 KB (3,786 words) - 06:49, 24 February 2024
...l y^{\alpha}}{\partial x^{i}} \frac{\partial y^{\alpha}}{\partial x^{j}}, \qquad (\star)
..._{1} \ldots i_{s - 1} k i_{s + 1} \ldots i_{p}}_{j_{1} \ldots j_{q}}}(x), \qquad k,i_{\alpha},j_{\beta} \in \mathbb{N}_{\leq n}.
6 KB (941 words) - 05:04, 11 December 2016
\gamma^{\alpha} \frac{\partial \psi}{\partial x^{\alpha}} - \mu \psi = 0, \qquad \alpha \in \{ 0,1,2,3 \},
...ial^{2} \psi}{\partial x^{\alpha} \partial x^{\beta}} + \mu^{2} \psi = 0, \qquad \alpha,\beta \in \{ 0,1,2,3 \}.
9 KB (1,306 words) - 18:13, 17 March 2023
|f (x_1, t) - f (x_2, t)|\leq M |x_1-x_2| \qquad \forall (x_1, t), (x_2, t)\in U \times [0,T]\,
e^{-Mt} |x_1-x_2| \leq |\Phi_t (x_1)-\Phi_t (x_2)| \leq e^{Mt} |x_1-x_2| \qquad \forall x_1, x_2\in \mathbb R^n\, .
5 KB (851 words) - 11:10, 30 November 2013
\exists n \in \omega_{0}: \qquad (p_{n} \Vdash \phi) \lor (p_{n} \Vdash \neg \phi).
* The relation $$ p \Vdash \phi(c_{1},\ldots,c_{n}), \qquad (\text{where } c_{1},\ldots,c_{n} \text{ are constants in } \mathcal{L}) $$
13 KB (2,070 words) - 12:25, 6 February 2021
...d} \quad \hat{r}_{i} = - \frac{\hbar}{i} \frac{\partial}{\partial p_{i}}; \qquad i \in \{ 1,\ldots,N \}.
6 KB (937 words) - 09:15, 14 December 2016
$$-y'' = q(x)y = \lambda y, \qquad a < x < b. \tag{1}$$
$$-y'' + q(x)y = \lambda y + f(x), \qquad a < x < b, \tag{2}$$
8 KB (1,288 words) - 05:22, 23 July 2018
J_{1/2} (x) = \sqrt{\frac{2}{\pi x}} \sin x \qquad J_{-1/2} (x) = \sqrt{\frac{2}{\pi x}} \cos x\, .
&& P_n (-x) = (-1)^n P_n (x) \qquad Q_n (-x) = (-1)^n Q_n (x)
6 KB (1,108 words) - 07:54, 26 March 2023
$$ \{f,gh\}=\{f,g\}h+g\{f,h\},\qquad \forall f,g,h\in C^\infty(M).$$
...s N}(x,y):=\{f(\cdot,y),g(\cdot,y)\}_M(x)+\{f(x,\cdot),g(x,\cdot)\}_N(y), \qquad \forall (x,y)\in M\times N.$$
6 KB (1,109 words) - 13:50, 12 December 2013
\omega\in\varLambda^2(M),\qquad \rd \omega=0,\qquad \forall v\in T_p M\quad \exists w\in T_p M:\ \omega_p(v,w)\ne0.
5 KB (856 words) - 05:41, 24 February 2022
$$H_{\text{dR}}^p (X/k) \cong H^p (X^\text{an}, \mathbf{C}), \qquad p \ge 0,$$
2 KB (380 words) - 01:16, 23 July 2018
\forall x \in \mathbf{R}: \qquad
\forall x \in \mathbf{R}, ~ \forall \omega \in \Omega: \qquad
9 KB (1,419 words) - 05:52, 15 June 2017
f(x) = \sum_n a_n (x-x_0)^n \qquad \forall x\in J
f(x) = \sum_n P_n (x-x_0)\qquad \forall x\in V\, .
6 KB (1,048 words) - 21:19, 14 January 2021
...{ 1 } , M _ { 2 } ) = \mathbf{v} ( M _ { 1 } ) \mathbf{v} ( M _ { 2 } ) , \qquad M _ { 1 } , M _ { 2 } \in \Gamma. \end{equation}
\begin{equation} \tag{a3} f | _ { k } ^ { \mathbf{v} } M = f , \qquad \forall M \in \Gamma. \end{equation}
13 KB (1,993 words) - 07:12, 15 February 2024
\left|\sum_{i=m}^n a_i\right| < \varepsilon \qquad \forall m, n \geq N\, .
3 KB (399 words) - 20:30, 8 December 2013
|f(x_1, t)- f(x_2, t)|\leq \omega (|x_1-x_2|) \qquad \mbox{for all } (x_1, t), (x_2, t)\in U\, .
3 KB (411 words) - 10:01, 29 November 2013
$$\frac{\sum_{k=1}^nX_k-A_n}{B_n},\qquad n=1,2,\dots,\label{*}\tag{*}$$
3 KB (488 words) - 20:56, 1 January 2019
\alpha (A)\leq \min \{\mu (A), \nu (A)\} \qquad \forall A\in\mathcal{B}
3 KB (399 words) - 17:27, 18 August 2012
$$R_n=\frac{2^{2n+1}[n!]^4}{(2n+1)[(2n)!]^3}f^{(2n)}(c),\qquad-1<c<1.$$
4 KB (614 words) - 21:36, 1 January 2019
|Du| (B) = \int_{-\infty}^\infty |D{\bf 1}_{U_t}| (B)\, dt \qquad\mbox{and}\qquad
16 KB (2,511 words) - 16:07, 12 October 2012
{L_{n}}(A \otimes_{R} B) = {\operatorname{Tor}^{R}_{n}}(A,B), \qquad
...= {\operatorname{Ext}_{\mathbb{Z} G}^{n}}(\mathbb{Z},A) \qquad \text{and} \qquad
12 KB (1,885 words) - 23:48, 23 April 2017
|f(x)-g(x)|=o(\operatorname{dist}(x,K)^k)\qquad \text{as }x\to K.
3 KB (555 words) - 09:11, 12 December 2013
|a_n-a_m| < \varepsilon \qquad \mbox{for every}\;\; n,m \geq N\, .
d(x_n,x_m) < \varepsilon \qquad \forall n,m \geq N\, .
8 KB (1,343 words) - 18:24, 9 December 2013
\dot z=A(t)z,\qquad z\in\R^n, \quad A(t)=\biggl(\frac{\partial v}{\partial x}(\gamma(t)\biggr),
\Omega(a)=\bigcap_{T<+\infty}\overline{\{g^t(a)|t\ge T\}},\qquad g^t(a)=\text{the flow map, }\left.\frac{\rd g^t(a)}{\rd t}\right|_{t=0}=v(a
7 KB (1,059 words) - 09:14, 1 October 2023
...(t)|\le C|t-t_*|^{-d},\quad\text{resp.,}\quad \|z_*(t)\|\le C|t-t_*|^{-d},\qquad 0<C,d<+\infty
5 KB (815 words) - 21:42, 31 July 2015
...all m\in\N\quad \lim_{z\to 0} \frac1{z^m}\Big(f(z)-\sum_1^m c_k z^k\Big)=0\qquad\text{as }z\to 0,\ z\in S.
3 KB (454 words) - 09:11, 12 December 2013
\nu (B) = \int_B f\, d\mu \qquad \forall B\in \mathcal{B}\, .
3 KB (484 words) - 12:09, 14 December 2012
\omega\land \rd f=f\Theta,\qquad f\in\mathscr O(\C^2,0),\ \Theta\in\Lambda^2(\C^2,0).
\lim_{t\to+\infty}\gamma(t)=0, \qquad \lim_{t\to+\infty}\frac{\gamma(t)}{\|\gamma(t)\|}=V\in\mathbb S^1=\{\|V\|=1
8 KB (1,340 words) - 09:03, 12 December 2013
g(f(x))=x\qquad &\forall x\in X\\
f(g(y))=y\qquad &\forall y\in Y\, .
10 KB (1,719 words) - 16:56, 30 November 2014
\cdots\cdots\qquad \\
\cdots\cdots\qquad \\
12 KB (2,085 words) - 22:05, 5 March 2012
\max_{0\le t\le 1}\sum_{k=1}^{2^n} |f_{2^n+k}(t)| \le C \sqrt{2^n}, \qquad n=0, 1, \dots, \quad C = 2^5\sqrt{3}
5 KB (754 words) - 21:07, 1 June 2013
\int_\eta^\beta |g(x)|\, dx < \varepsilon \qquad \forall \beta\in ]\eta, b[\, .
4 KB (598 words) - 21:45, 9 July 2013
f_k (x) \leq C + \varepsilon \qquad \forall k\geq k_0, \forall x\in K\, .
6 KB (1,001 words) - 18:22, 31 March 2017
\mu (A) = \sum_{x_i\in A} \alpha_i \qquad \mbox{for every Borel set } A\, .
5 KB (723 words) - 19:18, 14 November 2023
[ \dots [ [ s, t ] , t ] \dots t ] \qquad (p \textrm{ closing brackets} ) .
5 KB (722 words) - 18:41, 5 October 2023
|f^{(n)} (x)| \leq C n! R^n \qquad \forall x\in ]x_0-\delta, x_0+\delta[\quad \forall n\in \mathbb N\, .
4 KB (710 words) - 06:13, 13 June 2022
\forall i,j=1,\dots,k\qquad [v_i,v_j]=\sum_{s=1}^k
4 KB (678 words) - 15:17, 1 May 2014
...{2} \right] \geq \frac{[1 + b'(\theta)]^{2}}{I(\theta)} + {b^{2}}(\theta) \qquad (1)
5 KB (824 words) - 10:31, 16 July 2021
1\qquad & \mbox{if } x\in E\\
4 KB (627 words) - 18:12, 2 December 2013
...'_j]=0,\qquad [e_i,e'_j]=\begin{cases}1,\quad &i=j,\\0,&i\ne j,\end{cases}\qquad \forall i,j=1,\dots,n.
[v,w]=(Iv,w),\qquad I=\begin{pmatrix} 0_n&-E_n\\E_n&0_n\end{pmatrix},\quad I=-I^*,\ I^2=-E_{2n}
30 KB (4,754 words) - 19:19, 14 November 2023
\sum_{j=1}^{n}\frac{\partial L}{\partial x_j}x_j = 0;&\qquad \frac{\partial L}{\partial x_j} \geq 0,& j=1,\ldots,n;\\
\sum_{i=1}^{k}\frac{\partial L}{\partial y_i}y_i = 0;&\qquad \frac{\partial L}{\partial y_i} \leq 0,\quad y_i\geq 0,& i=1,\ldots,k.
12 KB (2,034 words) - 09:14, 9 June 2016
\qquad\text{resp.,}\qquad
\mathbf f\sim\mathbf h'\iff\exists h:\ h\circ f_i=f_i'\circ h,\qquad \forall i=1,\dots,r.
37 KB (5,881 words) - 19:10, 24 November 2023
$$N=\prod f_p,\qquad L(X,s) = \prod L_p(X,s)$$
$$y^2=x^3+{\bar\alpha}x+{\bar\beta}\qquad ({\bar\alpha}\equiv\alpha \;{\rm mod}\; p,\; {\bar\beta}\equiv\beta\;{\rm m
19 KB (3,251 words) - 20:37, 19 September 2017
$$G_{\alpha,S}\times_S S_1 \simeq G_{\alpha,S_1},\qquad G_{m,S}\times_S S_1 \simeq G_{m,S_1}$$
5 KB (831 words) - 21:59, 5 March 2012
$$A_n = \sum_{p \le n} \frac{f(p)}{p}, \qquad B_n^2 = \sum_{p^\alpha \le n} \frac{f^2(p^\alpha)}{p^\alpha}, \tag{2}$$
$$\sum_{|g(p)| \ge 1} \frac 1p < \infty, \qquad \sum_{|g(p)|<1} \frac{g^2(p)}{p} < \infty.$$
10 KB (1,718 words) - 04:55, 8 August 2018
\sum_{n=j}^k |a_n| < \varepsilon \qquad \left(\mbox{resp. } \sum_{n=j}^k \|a_n\|_A < \varepsilon \mbox{ in a Banach
5 KB (821 words) - 09:35, 16 August 2013
H_\alpha\circ H_\beta^{-1}:(v,b)\mapsto (H_{\alpha\beta}(b,v),b),\qquad H_{\alpha\beta}(\cdot,b)\in\operatorname{Homeo}(F)
H_{\alpha\beta}\circ H_{\beta\alpha}=\operatorname{id},\qquad H_{\alpha\beta}\circ H_{\beta\gamma}\circ H_{\gamma\alpha}=\operatorname{id
32 KB (5,299 words) - 12:27, 12 December 2020
# $\qquad\vdots$
# $\qquad\ldots$
19 KB (2,851 words) - 07:04, 7 March 2024
\{x\in\mathbb R : a\leq x <b\} \qquad \mbox{where } -\infty \leq a <b\leq \infty
6 KB (884 words) - 09:36, 16 August 2013
(\Box + m^{2}) u(x) = 0, \qquad
...partial_{0}^{2} - \partial_{1}^{2} - \partial_{2}^{2} - \partial_{3}^{2}. \qquad (1)
35 KB (5,270 words) - 23:26, 6 December 2016
f (x^+) :=\lim_{y\downarrow x} f (y) \qquad f (x^-):= \lim_{y\uparrow x} f(y)
1 \qquad &\mbox{if } x=0\\
49 KB (8,072 words) - 20:25, 12 March 2020
\int_\gamma \tau \cdot v = 0\qquad \mbox{for every continuous and piecewise } C^1 \mbox{ closed loop } \gamma\
5 KB (824 words) - 09:41, 29 January 2014
\right] \qquad (\ast)
6 KB (1,020 words) - 17:41, 4 May 2017
|a_1|\leq|a_2|\leq\dots,\qquad\lim_{n\rightarrow\infty}a_n=\infty,
6 KB (980 words) - 18:47, 24 May 2017
\forall f_{1},\ldots,f_{n} \in \mathcal{S}(\mathbf{R}^{d}): \qquad
...ambda} \mathopen{:} {\Phi_{\kappa}^{4}}(x) \mathclose{:} ~ \mathrm{d}{x}, \qquad \lambda \geq 0,
15 KB (2,298 words) - 22:02, 7 November 2017
\nu (A) = \int_A f\, \rd\mu \qquad \text{for every } A\in\mathcal{B}.
6 KB (957 words) - 07:56, 15 December 2016
{\rm Pearson}\qquad\qquad (y-\mu) / \sqrt{V(\mu)}
{\rm deviance}\qquad\qquad {\rm sgn}(y-\mu) \sqrt{\rm deviance}
30 KB (4,314 words) - 13:25, 30 May 2016
\qquad\qquad
18 KB (2,674 words) - 19:09, 16 December 2019
...}=(N-2)\int\limits_Sf(y)\frac{\cos(y-y_0,n_0)}{|y-y_0|^{N-1}}\,d\sigma(y),\qquad y_0\in S,$$
7 KB (1,142 words) - 21:30, 1 January 2019
\left|\int_\alpha^\beta f(x)\, dx\right| < \varepsilon \qquad \forall \beta>\alpha> \eta\, .
7 KB (1,076 words) - 12:30, 7 July 2013
, \qquad X^{\epsilon}_0=y.
d x_t = b(x_t ) dt\;,\qquad x_0=y.
13 KB (2,280 words) - 10:48, 28 October 2023
\forall x=(a_1,\dots,a_n)\in A^n,\ \forall w=(w_1,\dots,w_n)\in V\qquad t_w x=(a_1+w_1,\dots,a_n+ w_n).
\forall v\in T_aA,\ \forall w\in V,\qquad \rd t_w(a)\cdot v=v\in T_{t_w(a)}=T_{a+w} A.
16 KB (2,769 words) - 08:44, 12 December 2013
\right\}\qquad\tag{1} \end{equation}$$
6 KB (1,055 words) - 08:14, 22 May 2012
...in{array} { l } { \frac { d ^ { 2 } u } { d t ^ { 2 } } + A u = f ( t ) , \qquad t \in [ 0 , T ], } \\ { u ( 0 ) = u _ { 0 } , \frac { d u } { d t } ( 0 ) =
10 KB (1,449 words) - 17:45, 1 July 2020
dx_i(v)=v(x_i),\qquad v\in T_m M.
8 KB (1,509 words) - 05:24, 22 May 2017
\dslash_A \psi = 0, \qquad F^+ = -\frac12 \overline{\psi} \Gamma \psi,
&\qquad \left. - \frac{i}{8} \phi [\chi_{\mu\nu}, \chi^{\mu\nu}]
16 KB (2,663 words) - 10:57, 13 February 2024
\mu (A\cap M) + \mu (A\setminus M) = \mu (A) \qquad \forall A\in \mathcal{R}\, .
9 KB (1,397 words) - 10:08, 16 August 2013
u(t)=u_0+u_1t+u^2\,t^2+\cdots+u_n\,t^n+\cdots,\qquad u_0,u_1,\dots,u_n\in\R.
7 KB (1,080 words) - 09:14, 12 December 2013
$$z \mapsto \frac{az+b}{cz+d}, \qquad z \in \mathbf{C}, \qquad \begin{bmatrix} a & b \\ c & d \end{bmatrix} \in \SL_2(\mathbf{R}).$$
20 KB (3,146 words) - 02:52, 23 July 2018
A:D\to Y, \qquad \text{where } D \subset X.
14 KB (2,265 words) - 17:06, 24 January 2020
...}{f - x \frac{\partial f}{\partial x} - y \frac{\partial f}{\partial y}}, \qquad
11 KB (1,916 words) - 00:44, 12 August 2019
\frac{\partial \phi}{\partial x} = \frac{\partial \psi}{\partial y} \qquad \frac{\partial \psi}{\partial x} = - \frac{\partial \phi}{\partial y}\, .
f (z) = \sum_n a_n (z-z_0)^n\, \qquad \forall z\in U
61 KB (9,850 words) - 19:04, 20 January 2022
$$\PSL_2(\F_4) \cong \PSL_2(\F_5),\qquad \PSL_2(\F_7)\cong\PSL_3(\F_2),$$
12 KB (1,991 words) - 18:05, 29 November 2014
\mu (A) := \mathcal{H}^\alpha (A\cap E) \qquad \mbox{for } A\subset X \;\, \mathcal{H}^\alpha\text{-measurable}
10 KB (1,546 words) - 09:43, 16 August 2013
$$A^TI_{p,q}A = I_{p,q}\qquad\textrm{ where }I_{p,q} = \begin{pmatrix}1_p & 0 \\ 0 & -1_q\end{pmatrix}$$
14 KB (2,418 words) - 18:20, 7 November 2014
...eft[ \frac{d^{p-n}}{dv^{p-n}} \ln(x+e^vy)\right]_{v=0} \equiv 0 \pmod{p}, \qquad
16 KB (2,596 words) - 09:27, 13 February 2024
\right\}\qquad\tag{a1} \end{equation}$$
15 KB (2,514 words) - 20:27, 15 November 2017
\qquad y=0,1,2,\ldots;\;\mu>0
19 KB (2,808 words) - 10:20, 10 March 2024
\tr [\cov(\BETAT)] \le \tr [\cov(\BETA^{*})] , \qquad
22 KB (3,535 words) - 16:20, 10 March 2024
\begin{equation}\label{zerofree}\zeta(s)\neq0\qquad\text{ if }\sigma\geq1-\frac{A}{\ln^\alpha(\lvert t\rvert+2)}\text{ with }\a
$$ \zeta(1+it)=O\left(\ln^{2/3}\lvert t\rvert\right),\qquad\frac{1}{\zeta(1+it)}=O\left(\ln^{2/3}\lvert t\rvert\right),\quad \lvert t\r
45 KB (7,251 words) - 02:20, 29 June 2022
\dot x = \frac{\partial H}{\partial \psi}, \qquad -\dot\psi = \frac{\partial H}{\partial x} , \\
28 KB (4,182 words) - 07:56, 16 April 2023
\rho_U(u_\delta,u_T) \leq \delta, \qquad
33 KB (5,246 words) - 00:23, 25 April 2012