$$x=a\cos t,\quad y=a\sin t,\quad z=ht,$$
$$x=ce^{mt}\cos t,\quad y=ce^{mt}\sin t,\quad z=ce^{mt}\operatorname{cotan}\alpha,$$
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