formula stringlengths 5 635 | image stringlengths 80 86 |
|---|---|
( - 5 a ) + ( - 3 . 4 ) + ( + 3 . 5 ) + ( + 3 a ) + ( + 3 | 27278ab0-14e4-11e5-9192-001018b5eb5c__mathematical-expression-and-equation_10.jpg |
q _ { 0 } = + 0 . 8 0 0 7 8 , | 27a82360-3d62-11e8-baa7-5ef3fc9bb22f__mathematical-expression-and-equation_9.jpg |
( 4 1 x ) ^ { 2 } - ( 9 x ) ^ { 2 } = ( 3 0 x + 1 0 ) ^ { 2 } . | 2843c93c-88d4-4d53-875c-92e058da3079__mathematical-expression-and-equation_25.jpg |
\frac { \partial \sigma _ { 1 } ( \mathbf { v } _ { 1 } , t ) } { \partial t } = - \frac { 1 } { v } m M _ { 1 } \sum _ { j = 2 } ^ { N } \int d \mathbf { v } _ { j } \frac { \partial \Phi _ { 1 j } } { \partial \mathbf { v } _ { 1 } } \frac { \partial \phi _ { 2 } ^ { ( 1 j ) } } { \partial \mathbf { v } _ { 1 } } | 2856f826-d806-4f1f-992c-1e494a2d908d__mathematical-expression-and-equation_0.jpg |
( B - C ) \eta \xi + C \xi \prime \eta - A \eta \prime \xi = 0 | 28c60476-df3d-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg |
\tau = \frac { 2 u - ( 2 m + 1 ) } { 2 n + 1 } , | 28c604b5-df3d-11e1-7459-001143e3f55c__mathematical-expression-and-equation_0.jpg |
\int _ { 0 } ^ { \delta } \Phi ( x ) x ^ { \frac { 1 } { 2 } s - 1 } d x , \int _ { h } ^ { \infty } \phi ( x ) x ^ { \frac { 1 } { 2 } s - 1 } d x | 28c604c6-df3d-11e1-7459-001143e3f55c__mathematical-expression-and-equation_1.jpg |
p = \frac { \partial z } { \partial x } | 28f1a580-5d32-11e3-9ea2-5ef3fc9ae867__mathematical-expression-and-equation_11.jpg |
p _ { d } = \frac { 4 } { 5 } \alpha | 29002cb7-037a-48de-8ebb-7a2be3ce0824__mathematical-expression-and-equation_4.jpg |
\frac { R } { ( m + a ) ^ { 2 } } | 2939a170-1b94-11e4-8e0d-005056827e51__mathematical-expression-and-equation_4.jpg |
\frac { 1 } { 2 } \cdot \frac { m - 2 } { 2 } ( \frac { m - 2 } { 2 } + 3 ) = \frac { m ^ { 2 } + 2 m - 8 } { 8 } | 29a7639c-df3d-11e1-5298-001143e3f55c__mathematical-expression-and-equation_5.jpg |
N = C - S - H | 2a863820-0af6-11e5-b0b8-5ef3fc9ae867__mathematical-expression-and-equation_0.jpg |
+ \frac { 1 } { 2 } \frac { \partial ^ { 2 } u } { \partial z ^ { 2 } } \sum _ { i } \sum _ { k } ( m _ { i } c _ { i } ^ { 2 } + m _ { k } c _ { k } ^ { 2 } ) f ( \mu r ^ { 2 } ) | 2ad7710b-0f8c-48e7-821e-2c05b3a380e4__mathematical-expression-and-equation_5.jpg |
E = R _ { v } I + R I | 2b220600-d996-11e5-ac59-005056825209__mathematical-expression-and-equation_1.jpg |
7 \frac { 1 } { 2 } + 2 \frac { 1 } { 4 } = 9 \frac { 3 } { 4 } | 2bf6c701-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_19.jpg |
u _ { 1 } = u | 2db59880-df3d-11e1-5015-001143e3f55c__mathematical-expression-and-equation_8.jpg |
[ E ( z + 1 , p ) ] ^ { 2 } - [ E ( z - 1 , p ) ] ^ { 2 } = 4 z ^ { p } E \prime ( z , p ) | 2db5993d-df3d-11e1-5015-001143e3f55c__mathematical-expression-and-equation_6.jpg |
2 Q _ { n - 1 } = ( 1 + i x ) ^ { n - 1 } + ( 1 - i x ) ^ { n - 1 } | 2db599c0-df3d-11e1-5015-001143e3f55c__mathematical-expression-and-equation_9.jpg |
E = \frac { m a ^ { 2 } } { 2 \omega ^ { 2 } } \frac { 1 } { ( \frac { 1 } { x } - x ) ^ { 2 } + \frac { 4 b ^ { 2 } } { \omega ^ { 2 } } } | 2dc8cbc0-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_0.jpg |
- k ( x ^ { 2 } + y ^ { 2 } ) | 2df1075b-dbf5-11e6-a7df-001b63bd97ba__mathematical-expression-and-equation_5.jpg |
+ m [ ( l + l _ { 0 } + u ) ^ { 2 } \ddot { \phi } + 2 ( l + l _ { 0 } + u ) \dot { u } \dot { \phi } + ( l + l _ { 0 } + u ) g \sin \phi ] = 0 | 2e19abae-712c-11e2-83a5-005056a60003__mathematical-expression-and-equation_11.jpg |
\mu = \frac { 1 } { h \sqrt { 2 } } = \frac { 0 , 7 0 7 1 1 } { h } | 2e3bee70-ee52-11ea-9a6f-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg |
\phi _ { 2 } = x _ { 3 } , \phi _ { 3 } = x _ { 1 } ; | 2eadb482-df3d-11e1-1872-001143e3f55c__mathematical-expression-and-equation_5.jpg |
0 \le v \le n , | 2eadb503-df3d-11e1-1872-001143e3f55c__mathematical-expression-and-equation_12.jpg |
d = 0 . 2 5 | 2fe35530-452d-11e4-a450-5ef3fc9bb22f__mathematical-expression-and-equation_4.jpg |
T _ { 1 } = 2 7 3 + 2 6 . 7 | 3007b381-290b-11e8-8c71-001b63bd97ba__mathematical-expression-and-equation_7.jpg |
s = 6 + 0 . 0 0 2 l | 3026f900-e718-11e5-8d5f-005056827e51__mathematical-expression-and-equation_2.jpg |
\frac { d l n K } { d T } = - \frac { Q } { R T ^ { 2 } } | 304587f2-cf0a-4167-a7db-d667edee2473__mathematical-expression-and-equation_1.jpg |
- 2 \pi < \rho < 2 \pi , - \infty < y < + \infty | 30655015-df3d-11e1-1287-001143e3f55c__mathematical-expression-and-equation_15.jpg |
S = l i m \sum _ { a } ^ { b } x ^ { 2 } \Delta x | 30897b53-2a1c-4223-85e3-77c70237ba0a__mathematical-expression-and-equation_0.jpg |
f \prime _ { i n 1 } , f _ { i n 1 } , f _ { i n 2 } \in [ 0 . 1 , 1 . 0 ] | 317ec11a-8178-4ab0-8d1d-21361c153341__mathematical-expression-and-equation_9.jpg |
= \sum _ { n = 0 } \frac { \partial ^ { n } } { \partial t ^ { n } } [ D ^ { ( n ) } ( v ) + \frac { \partial W ^ { ( n ) } } { \partial x } - \frac { \partial U ^ { ( n ) } } { \partial z } + \Delta ( \frac { \partial \Theta ^ { ( n ) } } { \partial v } ) - \frac { \partial J ^ { ( n ) } } { \partial y } ] | 324ab161-df3d-11e1-1027-001143e3f55c__mathematical-expression-and-equation_7.jpg |
\{ A ^ { 2 } B ^ { 2 } C ^ { 2 } | \begin{array} { c c c } A ^ { 2 } , & A , & 1 \\ B ^ { 2 } , & A , & 1 \\ C ^ { 2 } , & C , & 1 \end{array} | + | \begin{array} { c c c } A ^ { 3 } , & A ^ { 2 } , & 1 \\ B ^ { 3 } , & B ^ { 2 } , & 1 \\ C ^ { 3 } , & C ^ { 2 } , & 1 \end{array} | - A B C | \begin{array} { c c c } A ^... | 324ab183-df3d-11e1-1027-001143e3f55c__mathematical-expression-and-equation_1.jpg |
= 4 s e n \frac { \beta - \gamma } { 2 } s e n \frac { \gamma - \alpha } { 2 } s e n \frac { \alpha - \beta } { 2 } | 324ab185-df3d-11e1-1027-001143e3f55c__mathematical-expression-and-equation_4.jpg |
1 6 + 4 = 2 0 | 32ba4150-1030-11e5-ae7e-001018b5eb5c__mathematical-expression-and-equation_1.jpg |
T _ { 0 } ^ { H } = ( 0 , 8 6 0 6 \pm 0 , 0 0 0 2 ) s | 33618f1b-c29b-4037-b3da-2a9a499a5f60__mathematical-expression-and-equation_1.jpg |
R = \frac { 1 \cdot 2 2 , 4 0 7 } { 2 7 3 , 1 } = 0 , 0 8 2 0 5 \frac { 1 \cdot \text { a t m } } { \text { g r a d } } | 33c822a0-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_3.jpg |
\tau _ { 2 } = \tau _ { 0 } \sqrt { 1 - K } | 341f3af5-aaa3-40fa-8a7f-103463cee081__mathematical-expression-and-equation_1.jpg |
K _ { e x t r } = \sum _ { i = 1 } ^ { p } ( \delta X _ { i } \prime ^ { 2 } + \delta Y _ { i } \prime ^ { 2 } ) | 3552fe12-3f4a-4c38-a095-1d0ca601f428__mathematical-expression-and-equation_10.jpg |
+ \epsilon k ^ { - 2 } \int _ { 0 } ^ { t } F _ { k } ( u ) ( \tau ) \sin k ^ { 2 } ( t - \tau ) d \tau , \text { f o r } k = 1 , 2 , \dots | 35a8c565-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_10.jpg |
S _ { m } = P - ( D - d ) ( V - v ) | 36a804d0-3b45-11e3-9053-005056825209__mathematical-expression-and-equation_1.jpg |
= ( F O + O P ) ^ { 2 } - ( F O - O P ) ^ { 2 } | 36e248a4-c073-11e6-ae7e-001b63bd97ba__mathematical-expression-and-equation_10.jpg |
d _ { \phi } ( \omega _ { 1 } \wedge \omega _ { 2 } ) = d _ { \phi } \omega _ { 1 } \wedge \omega _ { 2 } + ( - 1 ) ^ { p r } \omega _ { 1 } \wedge d _ { \phi } \omega _ { 2 } , | 36ff538c-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_3.jpg |
q _ { \mu } = W _ { \mu } + \mathbf { x } _ { 1 } + \mathbf { x } _ { 2 } + \dots + \mathbf { x } _ { \mu - 1 } | 37577c54-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_4.jpg |
+ [ l g \frac { ( n + 1 ) s - 1 } { n s - 1 } + J _ { 1 } ( ( n - 1 ) s - 1 ) ] \frac { 1 } { n - 1 ! } l g ^ { n - 1 } \frac { ( n + 1 ) s + t - 1 } { ( n + 1 ) s - 1 } + | 375d4960-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_7.jpg |
= \frac { ( \beta - 1 ) ( 2 n + \alpha + \beta - 2 ) - ( n + \beta - 1 ) ( n + \alpha + \beta - 2 ) } { 2 n + \alpha + \beta - 2 } | 37670cc7-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_10.jpg |
\frac { t g \alpha } { \alpha } = 1 ^ { * } ) | 37877fe0-9f32-43ac-bfb5-0d53df96d3aa__mathematical-expression-and-equation_12.jpg |
| \begin{array} { c c c c c } a _ { 1 } & 2 a _ { 2 } & 3 a _ { 3 } & 4 a _ { 4 } & 5 a _ { 5 } \\ o & \phi _ { 1 } ( x ) & ( x + a _ { 1 } ) \phi _ { 1 } ( x ) & ( x ^ { 2 } + a _ { 1 } x + a _ { 2 } ) \phi _ { 1 } ( x ) & ( x ^ { 3 } + a _ { 1 } x ^ { 2 } + a _ { 2 } x + a _ { 3 } ) \phi _ { 1 } ( x ) \end{array} | | 37985967-ff6a-4aa2-8d85-e98177e55f0c__mathematical-expression-and-equation_9.jpg |
= x + B \vee _ { p } C ( 0 ) = B \vee _ { p } C ( 0 ) + x | 37a92900-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg |
2 l h - v ( 2 l - d ) = \emptyset , | 37c50b96-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg |
\S 1 4 | 37c532ab-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_3.jpg |
\alpha = [ \alpha ] \cdot l \cdot \frac { p s } { 1 0 0 } = 0 . 6 6 4 9 l p s | 37d69c70-dadf-11e2-9439-005056825209__mathematical-expression-and-equation_0.jpg |
\frac { \epsilon } { 2 \pi } = \frac { \tau } { T _ { 2 } } = 0 , \frac { 2 } { 1 2 } , \frac { 4 } { 1 2 } , \frac { 6 } { 1 2 } , \frac { 8 } { 1 2 } , \frac { 1 0 } { 1 2 } | 37e9221c-df3d-11e1-1090-001143e3f55c__mathematical-expression-and-equation_1.jpg |
l = ( 1 1 0 ) \infty P ; s = ( 1 0 0 ) \infty P \infty ; x = ( 3 1 1 ) 3 P 3 | 37fc966d-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_0.jpg |
p V = \frac { 1 } { 3 } \mu c ^ { 2 } = R T , | 3800ea50-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_2.jpg |
A = \mathcal { F } _ { 1 } A _ { 1 } \pm \mathcal { F } _ { 2 } A _ { 2 } | 3818f820-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_2.jpg |
\beta = 0 . 1 8 9 3 7 \times 1 0 ^ { 1 0 } | 386913a1-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_2.jpg |
( Q , D _ { 0 } ) = Q \prod _ { q } ( 1 - ( \frac { D _ { 0 } } { q } ) \frac { 1 } { q } ) | 38b6beb8-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg |
\frac { 1 } { 2 \pi } \int _ { - \infty } ^ { \infty } k ^ { a + i x } \frac { d x } { a + i x } = \{ \begin{array} { c c } 0 & \text { p r o } k < 1 \\ 1 & \text { p r o } k > 1 \end{array} | 38feeb4e-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_8.jpg |
V \le k _ { 2 } L ^ { 3 } | 3903fdec-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg |
- \pi i R ( x _ { 0 } ) + ( \epsilon ) | 3904de86-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_7.jpg |
+ y _ { 2 } G _ { 3 } ( y _ { 3 } , \epsilon ) + y _ { 2 } ^ { 2 } \Psi _ { 1 } ( y , \epsilon ) + y _ { 3 } ^ { 2 } \Psi _ { 2 } ( y , \epsilon ) | 39b0deb9-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_10.jpg |
m = \frac { ( 1 - r _ { 2 } ) m _ { 1 } + ( 1 - r _ { 1 } ) m _ { 2 } } { ( 1 - r _ { 1 } ) + ( 1 - r _ { 2 } ) } | 39b0df11-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_0.jpg |
= \log \sin ( w + v ) \pi \cdot \sin ( w - v ) \pi + 2 ( w \log w - ( 1 - w ) \log ( 1 - | 39b43105-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_13.jpg |
\frac { a : \frac { 1 } { 1 \pm \alpha } } { b } = \frac { a ( 1 \pm \alpha ) } { b } | 39dd815e-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_2.jpg |
\frac { r _ { k - 1 } } { r _ { k } } = b _ { k - 1 } + b _ { k } \frac { r _ { k + 1 } } { r _ { k } } | 39de9313-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_0.jpg |
r ( I ^ { j } ) \ge \alpha | 3a5e8555-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg |
\frac { \partial b } { \partial a _ { 2 } } = b | 3b219a05-36ea-41c9-ae32-145d748c32e1__mathematical-expression-and-equation_6.jpg |
y _ { 0 } \prime \prime = f ( x _ { 0 } ) - \phi ( x _ { 0 } ) y _ { 0 } \prime - \psi ( x _ { 0 } ) y _ { 0 } | 3b713842-df3d-11e1-1090-001143e3f55c__mathematical-expression-and-equation_5.jpg |
\sigma _ { x } \sigma _ { \eta } = \sigma _ { \tau } | 3bb9a71a-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_2.jpg |
F = \sum _ { h = 1 } ^ { n } y _ { h } \overline { A } ( x ) _ { h } | 3c10016e-3105-11e9-8847-005056a2b051__mathematical-expression-and-equation_0.jpg |
g \equiv x - \frac { a } { 2 } = 0 | 3c550942-df3d-11e1-1431-001143e3f55c__mathematical-expression-and-equation_1.jpg |
( 1 + \alpha x ) ^ { \frac { 1 } { \alpha x } } = e ^ { \theta } | 3d127178-df28-11e1-4047-001143e3f55c__mathematical-expression-and-equation_3.jpg |
+ k _ { 2 } ( t , y ( h _ { 3 } ( t ) ) , y \prime ( h _ { 4 } ( t ) ) ) | 3d165157-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg |
x \in G _ { L } ( a , b ) | 3d1651a5-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_12.jpg |
y - m _ { 2 } x = 0 | 3da1f8f3-ebac-11ec-90b7-00155d01210b__mathematical-expression-and-equation_9.jpg |
t _ { 3 } = \sup X _ { 3 } | 3dc3d002-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg |
d \eta _ { i } / d t = \sum _ { j = 1 } ^ { n } \phi _ { j } ( \zeta _ { i j } ) - \rho _ { i } ( \eta _ { i } ) , | 3e087085-7a41-4006-b159-0a2e10718893__mathematical-expression-and-equation_1.jpg |
\text { t í } \lim \mathbf { a } ^ { \mu \nu } = \mathbf { a } _ { \mu \nu } , 1 \le \mu \le r , \nu = 1 , 2 , \dots , \alpha _ { r - \mu + 1 } . | 3e71ea15-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_6.jpg |
\log b = \log c + \log \cos \alpha | 3e7c3820-ad11-4f01-a7e6-2408915dddc8__mathematical-expression-and-equation_5.jpg |
u _ { n } = \alpha a ^ { n } + \beta b ^ { n } | 3ea4c46b-df3d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg |
c ^ { 8 } - 2 c ^ { 7 } + 3 c ^ { 6 } - 3 c ^ { 5 } + 2 c ^ { 4 } - c ^ { 3 } + 2 c ^ { 2 } - 2 c + 1 = 0 | 3f277f37-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_46.jpg |
\frac { \lambda _ { b } } { \lambda _ { a } } = ( a b ) | 3f3ca460-df28-11e1-1154-001143e3f55c__mathematical-expression-and-equation_6.jpg |
9 x ^ { 2 } - 4 y ^ { 2 } + 4 y z - z ^ { 2 } | 3f3f122c-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_11.jpg |
2 x - 4 y + 9 z = 2 8 | 3f3fadba-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_31.jpg |
| i n d _ { h } z _ { 1 } - i n d _ { h } z _ { 2 } | = 1 | 3fdf0e1f-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_1.jpg |
\lim _ { \Theta \rightarrow \frac { \omega } { 2 } } \int _ { 0 } ^ { 1 } [ f _ { 1 2 } ( r ) - u _ { 2 } ( r , \Theta ) ] ^ { 2 } r ^ { 2 \gamma - 1 } d r = 0 | 3fdf0ed8-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_6.jpg |
s _ { 1 } ^ { 1 } = \frac { 1 } { 2 } g \sin \alpha t ^ { 2 } | 3fec87d0-04d1-11e5-bdc1-001018b5eb5c__mathematical-expression-and-equation_2.jpg |
r _ { i } = [ \frac { n + k } { k } ] \text { p r o } j < i \le k , \text { k d e } j = k [ \frac { n + k } { k } ] - n | 4094a233-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg |
A x = f | 414afb0d-408b-11e1-2238-001143e3f55c__mathematical-expression-and-equation_5.jpg |
u _ { 1 } \prime = - ( \frac { h n ^ { 2 } \sin n t } { \omega } + \frac { 1 } { 3 } \frac { n ^ { 2 } + 2 } { n } \cot { n t } ) u + \frac { b } { \omega } u ^ { 2 } | 41fe1d79-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg |
- M ( x ) \rightarrow P ( x ) , S ( \iota ) \rightarrow M ( \iota ) \vdash S ( \iota ) \rightarrow P ( \iota ) : | 42109d9e-6183-49d7-9d40-c6f21a685579__mathematical-expression-and-equation_18.jpg |
\{ s \in \mathbb { R } ; ( t , s ) \in \Psi \} | 42a8f853-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_9.jpg |
C \prime = ( p _ { 1 } + \beta \prime ) \mathbf { u _ { 1 } } + ( p _ { 2 } + \beta q ) \mathbf { u _ { 2 } } + \beta c _ { 1 } \mathbf { u _ { 3 } } + \sqrt { ( 1 - p _ { 1 } ^ { 2 } - p _ { 2 } ^ { 2 } ) } \mathbf { u _ { 5 } } | 42b33c6a-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_11.jpg |
\mathbf { P _ { v 1 } } , \dots , \mathbf { p _ { v n } } ) ( \mathbf { x } _ { \mathbf { v } } - \mathbf { a } ) = \mathbf { A } ( \mathbf { x _ { v } } ) ( \mathbf { x _ { v } } - \mathbf { a } ) - \mathbf { P } ^ { - 1 } ( \mathbf { x _ { v } } ) ( \mathbf { F } ( \mathbf { p _ { v 1 } } , \dots , \mathbf { p _ { v ... | 42b33e05-408b-11e1-1586-001143e3f55c__mathematical-expression-and-equation_14.jpg |
k \prime ( t ) = - \frac { 1 } { u ( t _ { 1 } + \omega ) } ( u \prime ( t _ { 1 } + \omega ) - 1 ) ( u ( t _ { 1 } + \omega ) v \prime ( t ) - u \prime ( t ) v ( t _ { 1 } + \omega ) ) | 4365e0fb-f33d-11e1-1586-001143e3f55c__mathematical-expression-and-equation_9.jpg |
f ( x ) = \sum _ { j = 0 } ^ { n } [ a _ { j } x ^ { n - j } / j ! ( n - j ) ! ] | 4371aa6c-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_8.jpg |
| \omega ( t ) - \omega ( t _ { 0 } ) | = | \lambda _ { n } ( t ) - \gamma ( t _ { 0 } ) | \le | 4371ab44-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_0.jpg |
P ^ { ( n ) } ( G _ { - \epsilon } ) \rightarrow \sqrt { ( \frac { q _ { 1 } , \dots , q _ { k } } { ( 2 \pi ) ^ { k - 1 } \sum p _ { i } q _ { i } } ) } \int _ { G _ { - \epsilon } } e ^ { - \frac { 1 } { 2 } \sum q _ { i } x _ { i } ^ { 2 } } d v | 4371ac01-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg |
a + ( + b ) + ( + c ) + ( - d ) + ( + m ) | 43d27151-2259-11ea-8d84-001b63bd97ba__mathematical-expression-and-equation_4.jpg |
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