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