...ll y \exists z (x \le z \& z \le y), \quad \exists z(1 \le z \& z \le 4), \quad 1 \le 2\]
\[\exists z(x \le z \& z \le y), \quad z \le 1\]
1 KB (203 words) - 05:16, 21 June 2013
$$f^{(k)}(x_0)=P_n^{(k)}(x_0),\quad k=0,\dotsc,n.$$
...style="width:94%;text-align:center;">$f(x)-P_n(x)=o\left((x-x_0)^n\right),\quad x\to x_0,$</td> <td valign="top" style="width:5%;text-align:right;">(*)</td
1 KB (233 words) - 17:01, 16 March 2013
$$ \phi_i(t) = \{ \phi_i^1(t), \ldots , \phi_i^n(t) \}, \quad i = 1, \ldots, n \tag{1} \label{eq-1} $$
W ( \phi _{1} (t), \dots, \phi _{n} (t) ) \quad \equiv \quad 0,\quad\quad
6 KB (889 words) - 12:21, 19 March 2023
$$f(x_0+h)-f(x_0)=o\left(\frac{1}{\log1/|h|}\right),\quad|h|\to+0,$$
$$a_n,b_n=O(n^{-\delta}),\quad n\to+\infty,$$
861 bytes (143 words) - 17:25, 19 September 2014
$$\cos z=\frac{e^{iz}+e^{-iz}}{2},\quad\sin z=\frac{e^{iz}-e^{-iz}}{2i}.$$
$$\cos x=\frac{e^{ix}+e^{-ix}}{2},\quad\sin x=\frac{e^{ix}-e^{-ix}}{2i}$$
1 KB (171 words) - 12:50, 10 August 2014
$$(R(g)f)(g_1)=f(g_1g),\quad g,g_1\in G,\quad f\in E,$$
$$(L(g)f)(g_1)=f(g^{-1}g_1),\quad g,g_1\in G,\quad f\in E,$$
2 KB (386 words) - 07:53, 30 November 2014
B(p,q) = \frac{q-1}{p+q-1}B(p,q-1), \quad q > 1.
B(p,1-p) = \frac{\pi}{\sin p\pi}, \quad 0 < p < 1.
1,009 bytes (161 words) - 17:31, 11 November 2023
$$0\leq x\leq1,\quad a>0,\quad b>0,$$
$$I_x(a,a)=\frac12I_{1-y}\left(a,\frac12\right),\quad y=4\left(x-\frac12\right)^2,\quad0<x\leq\frac12.$$
2 KB (393 words) - 15:50, 31 March 2017
$$\phi_{n+1}(x)=o(\phi_n(x)),\quad x\to x_0,\quad x\in M,$$
1,018 bytes (175 words) - 19:31, 13 April 2024
$$\dot x=f(x),\quad f\in C^1(G),\quad G\subset\mathbf R^n.$$
1 KB (167 words) - 15:27, 22 September 2014
$$x'=x-v_xt,\quad y'=y-v_yt,\quad z'=z-v_zt,\quad t'=t,$$
2 KB (317 words) - 16:38, 30 July 2014
$$x=f(t),\quad y=g(t),\quad z=h(t),$$
946 bytes (164 words) - 17:20, 30 July 2014
\text{div } \mathbf{v} = 0 \quad \text{or} \quad \frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} + \frac{\
1 KB (175 words) - 12:28, 30 December 2018
$$\phi(x_1,\dots,x_n)=0,\quad\psi(x_1,\dots,x_n)=0$$
\begin{equation}\dot x_i(s)=Q_{\xi_i},\quad\dot\xi_i=-Q_{x_i},\quad i=1,\dots,n.\label{*}\end{equation}
3 KB (419 words) - 22:32, 10 December 2018
$$x=-f'(t),\quad y=-tf'(t)+f(t),\quad a<t<b;\label{2}\tag{2}$$
$$y=Cx+f(C),\quad C\in(a,b),\label{3}\tag{3}$$
3 KB (414 words) - 17:31, 14 February 2020
$$x=x(u),\quad y=y(u),\quad z=z(u),$$
1 KB (233 words) - 16:51, 8 April 2023
$$x=x(u),\quad y=y(u),\quad z=z(u),$$
1 KB (215 words) - 09:43, 15 August 2023
$$\{x_i\}_0^{n+1}\subset Q,\quad a\leq x_0<x_1<\ldots<x_{n+1}\leq b,$$
2 KB (297 words) - 18:38, 26 September 2014
x ^ {( k ) } = x ( x - 1 ) \dots ( x - k + 1 ) , \quad k \geq 1,
} , \quad n \geq k \geq 1,
3 KB (372 words) - 22:15, 5 June 2020
$$x=f_1(t),\quad y=f_2(t),\quad z=f_3(t),$$
1 KB (238 words) - 17:50, 13 August 2023
$$x=a\cos t,\quad y=a\sin t,\quad z=ht,$$
$$x=ce^{mt}\cos t,\quad y=ce^{mt}\sin t,\quad z=ce^{mt}\operatorname{cotan}\alpha,$$
3 KB (537 words) - 15:42, 29 September 2014
(AB)_{ik} = \sum_{j=1}^n a_{ij} b_{jk}, \quad i=1,\ldots,m;\ \ j=1,\ldots,p.
(A \circ B)_{ij} = a_{ij} b_{ij}, \quad i=1,\ldots,m;\ \ j=1,\ldots,n.
2 KB (289 words) - 19:22, 11 November 2023
{\dot{x} } = f ( x ) , \quad x \in \mathbf R ^ {n} ,
{\dot{y} } = g ( y ) , \quad y \in \mathbf R ^ {n}
3 KB (414 words) - 19:37, 5 June 2020
$$\frac{1}{(q+1)^{n+1}}\sum_{k=0}^n\binom nkq^{n-k}S_k,\quad S_k=\sum_{n=0}^ka_n,$$
188 bytes (34 words) - 14:11, 23 July 2014
\[L(x_1)=f(x_1),\quad L(x_2)=f(x_2).\]
\[ f(x)-L(x)=\frac{f''(\xi)}{2}(x-x_1)(x-x_2),\quad \xi\in [x_1,x_2].\]
1 KB (234 words) - 21:21, 15 July 2012
$$f(x)=a(x-x_0)^n+o((x-x_0)^n),\quad a\neq0,$$
$$g(x)=b(x-x_0)^m+o((x-x_0)^m),\quad b\neq0;$$
2 KB (420 words) - 18:01, 3 August 2014
$$\lambda_{k+1}-\lambda_k>\theta\lambda_k,\quad k=0,1,\ldots,\quad \theta>0,$$
1 KB (203 words) - 06:24, 22 April 2012
$$\sin\alpha=\frac{PQ}{OP},\quad\cos\alpha=\frac{OQ}{OP},\quad\tan\alpha=\frac{PQ}{OQ}.$$
1 KB (229 words) - 14:42, 14 February 2020
n! \approx \sqrt{2\pi n}\; n^n e^{-n}, \quad n \rightarrow \infty,
\Gamma(z+1) \approx \sqrt{2\pi z}\; z^z e^{-z}, \quad
1 KB (205 words) - 15:21, 14 February 2020
\rho ( u ) = 1 \quad ( 0 \leq u \leq 1 ) ,
u \rho ^ \prime ( u ) = - \rho ( u - 1 ) \quad ( u > 1 ) .
2 KB (376 words) - 08:55, 10 November 2023
$$\{x_i\}_0^{n+1}\subset Q,\quad x_0<\dotsb<x_{n+1},$$
997 bytes (159 words) - 12:37, 14 February 2020
$$(\pm1,0,0),\quad(0,\pm1,0)\quad(0,0,\pm1);$$
2 KB (244 words) - 14:08, 30 July 2014
$$p(x)=\frac{(n\mu)^n}{\Gamma(n)}x^{n-1}e^{-n\mu x},\quad x>0,$$
$$\frac{\alpha^n}{\Gamma(n)}x^{n-1}e^{-\alpha x},\quad x>0.$$
2 KB (279 words) - 19:37, 4 December 2016
$$ \begin{equation} (Lu)(x,y)=Mu-Nu=0, \quad x \in \mathbf{R}^n, \quad y \in \mathbf{R}^m, \label{1}\tag{1} \end{equation} $$
$$Mv+\lambda v=0,\quad Nw+\lambda w=0.\label{3}\tag{3}$$
4 KB (653 words) - 15:15, 14 February 2020
...e t \le 1} |f(t) - S_n(t, f)| \le 8 \omega \left( \frac{1}{n}, f \right), \quad n=1, 2, \dots
...mega \left( \frac{1}{2^m}, f \right), \quad n=2^m+k,\quad k=1, \dots, 2^m,\quad m=0, 1, \dots,
5 KB (754 words) - 21:07, 1 June 2013
\chi_1(t) \equiv 1\quad \text{ on } [0,1];
\chi_n = \begin{cases} \sqrt{2^m} \quad &&\text{ for } t\in\left(\frac{2k-2}{2^{m+1}}, \frac{2k-1}{2^{m+1}} \right
6 KB (1,003 words) - 05:01, 23 July 2018
\quad \text{and} \quad
2 KB (275 words) - 15:05, 14 February 2017
$$u_{xx}-y^mu_{yy}=0,\quad y>0,\quad0<m=\mathrm{const}<1,$$
$$u_{xx}-y^mu_{yy}+au_x+bu_y+cu=0,\quad y>0,\quad m>0,$$
3 KB (535 words) - 22:45, 10 December 2018
...1 } } { \nu _ { 2 } } x \right) ^ { ( \nu _ { 1 } + \nu _ { 2 } ) / 2 } , \quad x > 0, \end{equation*}
\begin{equation*} \frac { \nu _ { 2 } } { \nu _ { 2 } - 2 } \quad \text { for } \nu _ { 2 } > 2 \end{equation*}
7 KB (873 words) - 07:45, 27 January 2024
$$\sum_{k=0}^\infty u_k=s(P),\quad\lim s_n=s(P),\quad P-\lim s_n=s,$$
$$\sum_{k=0}^\infty u_k\quad\text{and}\quad\sum_{k=0}^\infty v_k$$
4 KB (617 words) - 17:36, 14 February 2020
$$|(z-z_1)\dotsm(z-z_n)|=r^n,\quad r>0,\quad z=x+iy.$$
2 KB (304 words) - 06:49, 7 April 2023
$$\frac{dx^i}{dt}=v^i,\quad\frac{dv^i}{dt}=f^i(x^1,\dots,x^n,v^1,\dots,v^n),\quad i=1,\dots,n,$$
$$f^i=\sum\Gamma_{jk}^i(x^1,\dots,x^n)v^jv^k,\quad\Gamma_{jk}^i=\Gamma_{kj}^i.\label{*}\tag{*}$$
3 KB (468 words) - 15:19, 14 February 2020
$$\gamma\geq0,\quad-\infty<\beta<\infty,$$
$$\phi_j(t)=\exp(-\gamma_jt^2+i\beta t),\quad\gamma_j\geq0,\quad-\infty<\beta<\infty.$$
4 KB (647 words) - 19:21, 24 March 2023
$$\def\rk{\textrm{rk}\;}\rk(f-E) = 1\quad\textrm{and}\quad \textrm{Im}(f - E)\subseteq \ker(f-E),$$
2 KB (271 words) - 20:19, 5 March 2012
$$x=\frac{x_1+\lambda x_2}{1+\lambda},\quad y=\frac{y_1+\lambda y_2}{1+\lambda}.$$
457 bytes (76 words) - 09:24, 13 April 2014
...a\in\Theta_0}\beta^*(\theta)=\alpha,\quad\beta^*(\theta)\geq\beta(\theta),\quad\theta\in\Theta_1,$$
2 KB (319 words) - 11:19, 13 August 2014
...bers $ a_i, b_i, \quad i = 1, \dots, n $. For complex numbers $ a_i, b_i, \quad i = 1, \dots, n$, it reads
2 KB (248 words) - 09:09, 31 May 2016
e _ {i} e _ {j} + e _ {j} e _ {i} = 0, \quad i \neq j,
e _ {i} ^ {2} = 1, \quad i = 1 \dots p,
9 KB (1,297 words) - 17:44, 4 June 2020
$$\left(\frac{-1}{p}\right)=(-1)^{(p-1)/2}\quad\text{and}\quad\left(\frac2p\right)=(-1)^{(p^2-1)/8}.$$
2 KB (295 words) - 17:43, 19 December 2014
$$S=\int\limits_{P_0}^{P_1}\sqrt{2(U+h)}ds,\quad ds^2=\sum_{i,j=1}^na_{ij}dq_idq_j$$
$$T=\frac12\sum_{i,j=1}^na_{ij}\dot q_i\dot q_j,\quad\dot q_i\equiv\frac{dq_i}{dt}.$$
2 KB (288 words) - 09:49, 5 August 2014
$$\sup_{x\in X}\inf_{y\in Y}F(x,y),\quad\max_{x\in X}\min_{y\in Y}F(x,y),\quad\text{etc.}\label{*}\tag{*}$$
2 KB (318 words) - 17:19, 14 February 2020
} \right ] , \quad t \geq 0,
F ( t \mid S ) = F ( a ( t ) \mid S _ {u} ) , \quad t \geq 0.
6 KB (853 words) - 21:12, 4 April 2020
$$AB=I_m,\quad BA=I_n,\quad m\neq n,$$
2 KB (351 words) - 12:24, 14 February 2020
$$A(x)\phi(x)+\int\limits_DK(x,s)\phi(s)ds=f(x),\quad x\in D.$$
378 bytes (72 words) - 16:46, 7 July 2014
$$\left\lbrace\sqrt\frac2\pi\cos nx\right\rbrace,\quad n=0,1,\ldots,$$
500 bytes (88 words) - 18:23, 14 August 2014
$$X'=A(t)X,\quad t\in\mathbf R,\label{1}\tag{1}$$
$$x'=F(t)x+G(t)u,\quad x\in\mathbf R^n,\quad u\in\mathbf R^m,$$
4 KB (628 words) - 17:38, 14 February 2020
$$\left(\frac pq\right)\quad\text{and}\quad\left(\frac qp\right)$$
2 KB (304 words) - 19:26, 14 August 2014
\sigma_n^k = \frac{S_n^k}{A_n^k} \rightarrow S, \quad n \rightarrow \infty,
\sum_{n=0}^\infty A_n^k x^n = \frac{1}{(1-x)^{k+1}}, \quad
3 KB (519 words) - 15:44, 7 May 2012
$$u_{rr}=\frac{\partial u_r}{\partial r},\quad u_{\theta\theta}=\frac1r\frac{\partial u_\theta}{\partial\theta}+\frac{u_r}
...ad u_{\phi\phi}=\frac1r\frac{\partial u_\phi}{\partial\phi}+\frac{u_r}{r},\quad u_{zz}=\frac{\partial u_z}{\partial z},$$
4 KB (616 words) - 15:37, 14 February 2020
$$\dot x=F(x),\quad x\in\mathbf R^n,\quad F(0)=0,\label{*}\tag{*}$$
2 KB (299 words) - 15:31, 14 February 2020
$$\def\a{\alpha}\def\b{\beta}(\a\b)(g) = \a(g)\b(g),\quad g\in G,\quad \a,\b\in X(G),$$
$$X(T)\simeq \Z,\quad X(\Z)\simeq T,\quad X(\R) \simeq \R,\quad X(G)\simeq G $$
5 KB (750 words) - 20:22, 17 August 2015
$$\cos\frac{2\pi}{b-a}kx,\quad\sin\frac{2\pi}{b-a}kx,\quad k=0,\dots,N-1.$$
2 KB (295 words) - 17:35, 24 March 2018
$$a_n=2r_n\tan\frac\pi n,\quad S_n=nr_n^2\tan\frac\pi n.$$
474 bytes (96 words) - 15:30, 13 October 2014
B(p,q) = \int_0^1 x^{p-1}(1-x)^{q-1}\rd x, \quad p,q > 0,
431 bytes (67 words) - 21:21, 29 April 2012
\| f \|_p = \left[ \int_E |f(x)|^p \; dx \right]^{1/p}, \quad f \in L_p(E)
491 bytes (78 words) - 21:36, 29 May 2016
\eta(\xi) = \Phi(x)y(x),\quad
\xi = \int_\alpha^x \sqrt{r(t)}\,\mathrm{d}t, \quad
2 KB (276 words) - 00:23, 30 July 2012
\{x_k\} \sim \{y_k\} \quad \iff \quad \lim_{k\to\infty} d (x_k, y_k)= 0\, .
2 KB (340 words) - 15:24, 18 October 2014
...ac{1}{k_n}\int\limits_S\nu(y)\frac{\partial}{\partial n_x}E_n(x,y)dS(y)=0,\quad x\in S,\label{1}\tag{1}$$
$$E_2(x,y)=\ln\frac{1}{|x-y|},\quad E_n=\frac{1}{|x-y|^{n-2}}$$
5 KB (913 words) - 15:34, 14 February 2020
$$u=\frac{4x}{x^2+y^2},\quad v=\frac{4y}{x^2+y^2}$$
698 bytes (110 words) - 15:19, 17 July 2014
..._1}{\b_1}\cdots\binom{\a_n}{\b_n}=\frac{\a!}{\b!(\a-\b)!},\qquad \text{if}\quad \a\geqslant\b.
...partial}{\partial x_1},\dots,\frac{\partial}{\partial x_n}\biggr)=\partial\quad\text{if the choice of $x$ is clear from context.}
3 KB (512 words) - 06:16, 13 June 2022
$$k=0,\ldots,n-1,\quad\phi=\arg\left(-\frac ba\right).$$
524 bytes (94 words) - 17:30, 23 December 2014
$$x=\operatorname{ci}(t),\quad y=\operatorname{si}(t),$$
910 bytes (138 words) - 19:17, 11 January 2024
$$u_{tt}-\Delta u+\frac{\lambda(t,x)}{t}u_t=0,\quad t\neq0,$$
$$u(t,x)\bigg|_{t=0}=\phi(x),\quad u_t(t,x)\bigg|_{t=0}=0,$$
3 KB (478 words) - 11:53, 20 April 2012
x = v \quad y = c \cosh \frac{v}{c} \sin u \quad z = c \cosh \frac{v}{c} \cos u\, .
2 KB (303 words) - 20:07, 12 November 2023
$$x''+p(t)x'+q(t)x=0,\quad p\in C^1,\quad q\in C,\label{2}\tag{2}$$
2 KB (337 words) - 17:29, 14 February 2020
$$A\times_C B,\quad A\times_{\a,\b}B, \quad \textrm{ or }\quad A\prod_{\a,\b} B.$$
3 KB (575 words) - 10:30, 23 November 2013
$$v=\frac{q^{n+1}-1}{q-1},\quad k=\frac{q^n-1}{q-1},\quad\lambda=\frac{q^{n-1}-1}{q-1}.$$
$$v=p^r=4t-1,\quad k=2t-1,\quad\lambda=t-1.$$
5 KB (832 words) - 10:37, 15 November 2014
...right) \Gamma \left(n+1 - \textstyle{\frac{m}{2}}\right)} - {\bf H}_n (x) \quad \mbox{for }\; n\geq 0
...1}}{\Gamma \left(m + \textstyle{\frac{3}{2}}\right)} - {\bf H}_{-n} (x)\, \quad \mbox{for }\; n > 0\, ,
5 KB (721 words) - 08:49, 22 February 2014
$$\pi(x)>\operatorname{li}x-ax\ln^{-m}x,\quad\pi(x)<\operatorname{li}x+ax\ln^{-m}x$$
$$\theta(x)=\sum_{p\leq x}\ln p,\quad\psi(x)=\sum_{p^m\leq x}\ln p,$$
3 KB (542 words) - 16:58, 14 February 2020
\frac{x}{a}\left(1+\frac{x}{a}\right) = 1 \quad \text{or} \quad x = \frac{a}{1+\frac{x}{a}}
2 KB (325 words) - 21:24, 3 April 2015
$$u(x)=\phi(x),\quad x\in S,$$
810 bytes (116 words) - 14:55, 16 October 2014
x = \rho \cos t \quad y = \rho \sin t \quad z = \rho \arctan \alpha + kt\, .
2 KB (310 words) - 19:56, 12 November 2023
$$\inf[a,b]=a,\quad\sup[a,b]=b;$$
$$\inf(a,b)=a,\quad\sup(a,b)=b;$$
4 KB (722 words) - 19:45, 7 January 2015
$$v_x=\frac{\partial\psi}{\partial y},\quad v_y=-\frac{\partial\psi}{\partial x}.$$
903 bytes (145 words) - 15:08, 30 July 2014
$$f,g\in L^\#,\quad x\in L,\quad \l\in k.$$
$$x=\sum_{i=1}^n\l_{\nu_i}e_{\nu_i},\quad \l_{\nu_i}\in k,\quad
5 KB (903 words) - 21:31, 3 January 2021
$$x^{k+1} = x^k - \def\a{\alpha} \a_k f'(x^k),\quad k = 0,1,\dots ,$$
$$x^{k+1} = x^k - \a_k(Ax^k -f), \quad k = 0,1,\dots ,$$
3 KB (519 words) - 19:10, 6 April 2012
$$\dot z=A(t)z,\quad z\in\CC^n,\ A(t)=\|a_{ij}(t)\|_{i,j=1}^n$$
|y_*(t)|\le C|t-t_*|^{-d},\quad\text{resp.,}\quad \|z_*(t)\|\le C|t-t_*|^{-d},\qquad 0<C,d<+\infty
5 KB (815 words) - 21:42, 31 July 2015
$$x=\pi n,\quad n=0,\pm1,\pm2,\mathinner{\ldotp\ldotp\ldotp\ldotp}$$
824 bytes (127 words) - 14:15, 14 February 2020
$$\mathbf{E}X_j=0,\quad \mathbf{E}X_j^2=\sigma^2>0,\quad\mathbf{E}\lvert X_j\rvert^3<\infty.$$
2 KB (303 words) - 11:49, 23 November 2023
$$\sum_{j=1}^na_{ij}x_j=b_i,\quad i=1,\dots,m,$$
$$x_1\geq1,\quad x_2\geq1,\quad x_3\geq1,\quad t\geq3,$$
5 KB (700 words) - 19:16, 4 November 2014
F_x+F_y=F_{x+y};\quad\lambda F_x=F_{\lambda x},\quad\lambda\in K.
x=\sum_{\alpha}\lambda_\alpha x_\alpha,\quad\lambda_\alpha\in K,
14 KB (2,558 words) - 11:28, 21 June 2016
\[ g_k(\delta) = \frac{1}{\Gamma(1 + \delta k)}, \quad \delta > 0, \quad k = 0, 1, \dots, \]
2 KB (377 words) - 02:56, 2 June 2013
$$\rho=a\phi^2-l,\quad l\geq0.$$
750 bytes (121 words) - 19:26, 16 March 2023
...geq \frac { c _ { 1 } } { \operatorname { diam } \Omega } \cdot \omega , \quad c_ { 1 } = \frac { 2 \pi \alpha ( n - 1 ) } { \alpha ( n ) }, \end{equati
...{Vol} ( \Omega ) ^ { n - 1 } } \geq c _ { 2 } \cdot \omega ^ { n + 1 } , \quad c _ { 2 } = \frac { \alpha ( n - 1 ) ^ { n } } { \left( \frac { \alpha ( n
3 KB (378 words) - 16:56, 1 July 2020
$$\frac{\partial u(x)}{\partial n}=\phi(x),\quad x\in S,$$
885 bytes (129 words) - 07:13, 23 August 2014
$$(\Ad a)X = aXa^{-1}, \quad X\in T_e(G) = \g\subset \textrm{End}(V).$$
$$(\ad x)y = [x,y],\quad x,y\in \g,$$
3 KB (407 words) - 16:57, 27 March 2012
ax^2+bx+c=0,\quad a\ne0.
x_1+x_2=-\frac{b}{a},\quad x_1x_2=\frac{c}{a}.
2 KB (384 words) - 07:34, 18 December 2014
...}{\partial q},\quad\dot q=\frac{\partial H}{\partial p},\quad p=(p_1,p_2),\quad q=(q_1,q_2),\label{*}\end{equation}
4 KB (703 words) - 21:33, 23 November 2018
\rho = a\sqrt{\phi} + l,\quad l>0.
1 KB (165 words) - 05:44, 9 April 2023
$$\ln N=\frac{\lg N}{\lg e},\quad\lg N=\frac{\ln N}{\ln10},$$
$$\frac{1}{\lg e}=2.30258\dots,\quad\frac{1}{\ln10}=0.43429\dots.$$
3 KB (453 words) - 15:11, 19 August 2014