image imagewidth (px) 26 336 | latex stringlengths 2 482 | split stringclasses 4
values |
|---|---|---|
X ^ { n } - 1
| train | |
p
| train | |
1 5 4 \times 1 8 6 \leq 2 8 6 4 4
| train | |
e _ { \pi } M
| train | |
3 3
| train | |
\Delta - \sum B
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\frac { y } { q }
| train | |
b \geq \frac { 1 } { a - 1 }
| 2019 | |
\frac { 7 } { 6 } y _ { n } ( - y _ { n + 1 } + 2 y _ { n } - y _ { n - 1 } )
| 2014 | |
\sum t - \lambda
| train | |
P ( z ) = \frac { a z + b } { c z + d }
| 2016 | |
t
| train | |
e = 2
| train | |
\frac { p } { q }
| train | |
a = \sqrt { \frac { 5 } { 6 } }
| 2019 | |
a _ { n } = - \sum _ { k = 1 } ^ { n - 1 } c _ { n - k } a _ { n }
| 2016 | |
A t + \sqrt { o }
| train | |
z = r ( \cos \theta + i \sin \theta )
| train | |
\log _ { 2 } \frac { 1 } { 2 } + \log _ { 4 } \frac { 2 } { 4 }
| train | |
v , u _ { 1 } , u _ { 2 }
| train | |
\beta
| train | |
T _ { c }
| 2016 | |
a _ { 0 } + 3 a _ { 1 } + 9 a _ { 2 } + 2 7 a _ { 3 } = 0
| 2014 | |
( \frac { 1 } { 9 } , \frac { 1 } { 9 } )
| 2016 | |
B \geq 1 + y
| train | |
0 > r > - 1
| 2019 | |
\sqrt { 1 + \sqrt { 2 + \sqrt { 3 + \sqrt { 4 } } } }
| train | |
\sum _ { i = 1 } ^ { k } \frac { x ^ { a _ { i } } } { 1 - x ^ { b _ { i } } } = \frac { 1 } { 1 - x }
| train | |
1 9 \pm 7 1 / ( ( 1 8 1 - 1 0 8 ) \times 7 2 )
| train | |
( 2 a + b + 1 ) \times ( 2 a + b + 1 )
| 2016 | |
\frac { d } { d s } c _ { n } ( f , s ) = \frac { n } { s } c _ { n } ( f , s )
| train | |
( x ^ { 0 } , x ^ { 1 } , x ^ { 2 } , x ^ { 3 } , x ^ { 4 } ) = ( t , x , y , z , \theta )
| 2016 | |
- 3 x
| train | |
z _ { 1 } ^ { 2 } + 1 ^ { z } - z _ { 2 } ^ { 2 } + 2 ^ { z }
| train | |
\sqrt [ 5 ] { 5 5 }
| train | |
\frac { 1 } { 2 } \cos 2 \alpha
| 2019 | |
( n , e )
| train | |
\sum f _ { n }
| 2019 | |
\sum _ { m } f ( m + 3 )
| train | |
b \in T
| 2016 | |
r = \sqrt { \theta }
| train | |
a ( t _ { i } ( n ) ) \div n
| 2016 | |
\frac { \pi r ^ { 2 } h } { 3 }
| train | |
r = \alpha ( \theta ) \pm d
| train | |
[ b ^ { x } \{ ( \frac { a } { b } ) ^ { x } + 1 \} ] ^ { \frac { 1 } { x } }
| train | |
s _ { n } = \sum _ { k = 1 } ^ { n } a _ { k }
| train | |
\lim _ { x \rightarrow + \infty } a ^ { x } = 0
| train | |
7 6 . 1
| train | |
3 \times 4 \times 5 \times 6 = 3 6 0
| train | |
3 x - 5 < - 2
| train | |
\sin x - \sin y - \sin ( x - y )
| train | |
\sqrt { 2 } + \sqrt { 8 }
| 2014 | |
( 2 , 2 , 2 , 0 )
| 2014 | |
( n - 1 ) 2 ^ { n - 4 }
| train | |
\frac { 1 } { n ^ { 2 } } \leq \frac { 1 } { n - 1 } - \frac { 1 } { n }
| train | |
\{ \sigma , F \}
| train | |
\frac { \sin B + \sin C } { \cos B + \cos C }
| train | |
f ( x ) = \alpha _ { a b } x ^ { a } x ^ { b }
| 2019 | |
1 \times 1 + 1 \times 2 + 2 \times 2
| 2014 | |
\sum _ { k = 0 } ^ { 1 2 7 } ( k + 2 k ^ { 2 } )
| train | |
y _ { z }
| train | |
\sum _ { m } f ( m + 3 )
| train | |
\frac { 1 } { \sqrt { N } }
| 2019 | |
( ( 1 5 2 + 6 0 ) \div 5 1 ) \times 1 6 3 \neq - 4 2 0
| train | |
( 9 5 / 9 7 ) - 1 2 0 \neq - 8 9
| train | |
F _ { [ p + 2 ] } ^ { 2 } = F _ { [ p + 2 ] \alpha _ { 1 } \ldots \alpha _ { p + 2 } } F _ { [ p + 2 ] } ^ { \alpha _ { 1 } \ldots \alpha _ { p + 2 } }
| 2019 | |
e ^ { \int x ^ { 2 } d x }
| train | |
\frac { 4 } { q } + \frac { 4 } { 2 \pi - q } - ( \frac { 8 } { \pi } - \frac { \pi } { 2 } )
| 2016 | |
x ^ { i + 2 j \times k ^ { 3 } - 2 \frac { j } { i } }
| train | |
3 . 1
| train | |
\sqrt [ n ] { \frac { n + 1 } { ( n - 1 ) ^ { 2 } } }
| train | |
2 c > \sqrt { 6 } - \sqrt { 3 }
| 2016 | |
1 + \sqrt { 5 } = x _ { 1 } + y _ { 1 } \sqrt { 5 }
| 2014 | |
e ^ { \int x ^ { 2 } d x }
| train | |
( 1 2 - x ) ^ { 2 }
| train | |
6 + 6 + 1 6 = 2 8
| 2016 | |
x + ( - x ) = 0
| train | |
k w ^ { k - 1 } = 0
| train | |
\cos 3 \theta = 4 \cos ^ { 3 } \theta - 3 \cos \theta
| 2014 | |
2 . 7
| train | |
\sum _ { m = 0 } ^ { M } \sum _ { n = 0 } ^ { N } a _ { m , n }
| train | |
d _ { f r } = d _ { t c } + h _ { f r } - t _ { b r }
| train | |
1 8 6 \pm 6 + 9 8 + 1 7 6 + 9 2
| train | |
\frac { \sqrt { 5 } } { 3 }
| 2019 | |
a + b + c + d + e
| train | |
| \frac { a x _ { 0 } + b y _ { 0 } + c } { \sqrt { a ^ { 2 } + b ^ { 2 } } } |
| train | |
x = - n + f
| 2016 | |
\exists p ( k )
| 2016 | |
\lim _ { n \rightarrow \infty } \phi _ { n } = 0
| 2016 | |
P _ { 6 } ( x ) = x ^ { 2 } P _ { 4 } ( x ) = x ^ { 2 } ( x ^ { 2 } - a ^ { 2 } ) ( x ^ { 2 } - b ^ { 2 } )
| 2019 | |
v ^ { n } = \sum _ { i = 0 } ^ { n - 1 } ( - 1 ) ^ { i } \alpha ^ { n - 1 - i } \beta ^ { i }
| train | |
\int _ { w } ^ { T m } F d P
| train | |
\alpha ^ { 2 } + \beta ^ { 2 } = ( \alpha + \beta ) ^ { 2 } - 2 \alpha \beta
| 2014 | |
a ^ { x } a ^ { y } = a ^ { x + y }
| train | |
t ( p ^ { ( ( 7 ) ) } )
| train | |
6 ^ { 6 } \cdot 6 ^ { 2 } = ( 6 ^ { x } ) ^ { 4 }
| train | |
f o r a n y r o o t
| 2019 | |
\lim _ { n } \frac { 1 } { n } \sum _ { k = 0 } ^ { n - 1 } f ( X _ { k } )
| train | |
v _ { 2 n - 1 } ( 0 ) = \frac { 1 } { \sqrt { \pi } } \frac { ( - 1 ) ^ { n + 1 } } { \sqrt { 2 n - 1 } }
| 2019 | |
z
| train |
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