...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