formula stringlengths 5 635 | image stringlengths 80 86 |
|---|---|
\bar { A } _ { 1 } = E _ { U } t _ { U } + 2 E _ { C } s + E _ { L } t _ { L } = A _ { 1 } | 19993e80-3c62-11e1-1278-001143e3f55c__mathematical-expression-and-equation_5.jpg |
^ { 2 } i _ { s } = i ^ { \beta } = i ^ { \alpha } + i ^ { 0 } | 19993f56-3c62-11e1-1278-001143e3f55c__mathematical-expression-and-equation_13.jpg |
\Gamma ( \frac { 1 } { 2 } ) = 2 \int _ { 0 } ^ { \infty } e ^ { - z ^ { 2 } } d z = \sqrt { \pi } = 1 , 7 7 2 5 , | 16f52750-0a0b-11e3-9439-005056825209__mathematical-expression-and-equation_6.jpg |
\mathcal { F } _ { 1 } = \frac { a _ { 1 } } { a _ { 0 } } , \mathcal { F } _ { 2 } = \frac { a _ { 2 } } { a _ { 1 } } \cdot \frac { a _ { 1 } } { a _ { 0 } } , \dots \mathcal { F } _ { i } = \frac { a _ { i } } { a _ { i - 1 } } \cdot \frac { a _ { i - 1 } } { a _ { i - 2 } } \cdot \dots \cdot \frac { a _ { 1 } } { a... | 7271e233-d533-40fb-ac8c-76bbe7846005__mathematical-expression-and-equation_0.jpg |
D : \delta = f : f \prime | 85b46b02-a6c5-4852-ab64-0c29548c0a3b__mathematical-expression-and-equation_4.jpg |
\frac { d x } { d u } = \sum _ { \mu } \frac { u ^ { \mu } v ^ { \mu + 1 } } { \mu ! \Gamma ( s + \mu + 2 ) } | 3a0f70ab-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_4.jpg |
V \prime ( x ) U ^ { T } ( x ) - U \prime ( x ) V ^ { T } ( x ) = - E | 3a5e8490-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_5.jpg |
\omega ^ { 1 } = 0 | 47ac2050-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg |
\nabla ^ { 2 } \beta _ { i } - \frac { 1 + \mu } { 2 } ( \frac { \partial ^ { 2 } \beta _ { i } } { \partial x _ { j } ^ { 2 } } - \frac { \partial ^ { 2 } \beta _ { j } } { \partial x _ { i } \partial x _ { j } } ) - \frac { 2 G _ { c } } { E ^ { * } t ( h + s ) } ( \beta _ { i } + \frac { \partial w } { \partial x _ ... | 153e6f50-3c62-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg |
\text { i f } x ( i ) \le y ( i ) | 0b5a768d-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_9.jpg |
\overline { M } _ { k } = [ \mathfrak { M } _ { k } - M _ { k } ] | 1138eb4b-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg |
\mu ( \sigma ) = i \omega ( \sigma ) t | 9979c596-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_8.jpg |
H = H _ { 0 } + \Delta H = 1 2 3 1 - | 1e3fedb0-31e7-11e4-90aa-005056825209__mathematical-expression-and-equation_6.jpg |
+ 2 \frac { 3 } { 4 } + 3 \frac { 1 } { 4 } | 2bf6ee13-435f-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg |
v = 2 - 3 + 2 = 1 | 1f3c1383-290b-11e8-8c71-001b63bd97ba__mathematical-expression-and-equation_1.jpg |
H _ { e } ^ { A } = 4 I _ { s } [ \beta ( \frac { a ( \bar { z } - t ) } { \pi } + \frac { 1 } { 2 } ) - \beta ( \frac { a ( \bar { z } + t ) } { \pi } + \frac { 1 } { 2 } ) ] | 9a4ea250-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_6.jpg |
H _ { 1 } = - i \omega ^ { - 1 } P _ { 2 } ( x _ { 1 } , x _ { 2 } ) \frac { d Z _ { 2 } } { d x _ { 3 } } , H _ { 2 } = i \omega ^ { - 1 } P _ { 1 } ( x _ { 1 } , x _ { 2 } ) \frac { d Z _ { 1 } } { d x _ { 3 } } | 18f458c7-a428-4bb6-bde8-a20b7ce99f01__mathematical-expression-and-equation_10.jpg |
h ) \sqrt { 1 2 0 0 } ? | 6602b2cc-e3d9-11e6-9608-001b63bd97ba__mathematical-expression-and-equation_0.jpg |
G ^ { m q } _ { B \kappa s } ( \theta _ { 0 } ) = O _ { m \kappa } \{ - i \cdot 2 ^ { 2 m + 2 s } [ s ! ( m + s ) ! / ( 2 m + 2 s ) ! ] P ^ { m } _ { m + 2 s } ( \cos \theta _ { 0 } ) + \dots | 98a5f9e9-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_13.jpg |
U = \frac { A _ { \alpha } } { ( x - a ) ^ { \alpha } } + \frac { A _ { \alpha - 1 } } { ( x - a ) ^ { \alpha - 1 } } + \dots + \frac { A _ { 1 } } { x - a } + \frac { f _ { a } ( x ) } { \Phi _ { a } ( x ) } | 6ece1643-d8c7-11e6-a316-001b63bd97ba__mathematical-expression-and-equation_3.jpg |
[ m \cos ( M - N ) + n t ] ^ { 2 } = k ^ { 2 } . \sin ^ { 2 } \psi , | 26b0a400-3d62-11e8-baa7-5ef3fc9bb22f__mathematical-expression-and-equation_6.jpg |
B _ { 1 } ^ { 3 } = B _ { 3 } ^ { 1 } = - \frac { 1 } { 6 } ( 2 A \prime - 3 x ^ { 1 } ) | 0620b978-570b-11e1-1090-001143e3f55c__mathematical-expression-and-equation_12.jpg |
\mathcal { B } _ { 0 } = \frac { 4 } { 3 } | 973bf9b0-ee61-11ea-9a6f-5ef3fc9ae867__mathematical-expression-and-equation_5.jpg |
\times \int _ { k r _ { 1 } } ^ { k R _ { 0 } } J _ { m + 2 n + 1 / 2 } ( x ) H _ { q + 2 s + 3 / 2 } ^ { ( 1 ) } ( x ) ( d x / x ) + ( k R _ { 0 } ) ^ { - 1 / 2 } J _ { m + 2 n + 1 / 2 } ( k R _ { 0 } ) \times | 98a5f98c-4334-11e1-7963-001143e3f55c__mathematical-expression-and-equation_11.jpg |
n _ { 1 } , n _ { 2 } \in N | 36546d77-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_10.jpg |
\bar { Q _ { n } } = | V _ { n } | ^ { - 1 } \sum _ { t \in V _ { n } } Q _ { n } \circ \theta _ { t } | 0024bac0-ac0b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_3.jpg |
E ( X + Y ) = E ( X ) + E ( Y ) | 968e04b0-482f-11e4-a450-5ef3fc9bb22f__mathematical-expression-and-equation_7.jpg |
\lim _ { t \rightarrow \infty } \sup t ^ { n - 1 } \int _ { \gamma ( t ) } ^ { \infty } p ( x ) d x > 0 | 0028418f-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_2.jpg |
v _ { \nu } = \frac { x _ { 0 } - x _ { \nu } } { s _ { \nu } \prime } \Delta x + \frac { y _ { 0 } - y _ { \nu } } { s _ { \nu } \prime } \Delta y + \underbrace { ( s _ { \nu } \prime - s _ { \nu } ) } _ { l _ { \nu } } . | 0d97b18d-23df-cfa9-f837-18ecbb0cada6__mathematical-expression-and-equation_2.jpg |
c o s i = \sqrt { - \tan ( \alpha - \Omega ) \tan ( \beta - \Omega ) } | 0b4c5c2a-40e4-11e1-3052-001143e3f55c__mathematical-expression-and-equation_4.jpg |
\frac { \partial h } { \partial t } \xi \eta \zeta d t . | 89c86670-f710-11e9-94c9-001999480be2__mathematical-expression-and-equation_0.jpg |
[ x _ { 1 } ( \omega ) , \dots , x _ { n } ( \omega ) ] \in A | 4371abf6-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_2.jpg |
1 5 0 0 : 2 2 . 6 = 6 6 \text { r o u r } | 71c2566a-c1f2-11eb-a5d1-001b63bd97ba__mathematical-expression-and-equation_11.jpg |
b ^ { * } = - \frac { \beta } { \beta ^ { * } } \frac { \beta ^ { 4 } } { \beta ^ { * 4 } } b | 1a69faf6-3c62-11e1-1431-001143e3f55c__mathematical-expression-and-equation_8.jpg |
Q = \{ [ \xi _ { 1 } , \xi _ { 2 } ] \in R ^ { 2 } ; | \xi _ { 1 } - \frac { 1 } { 2 } | + | \xi _ { 2 } | \le \frac { 1 } { 2 } \} | 34fd1bdc-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg |
\omega _ { 1 } \prime = 2 K \lambda , | 37f172d9-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_9.jpg |
H _ { \beta } ^ { \gamma } \circ H _ { \alpha } ^ { \beta } = H _ { \alpha } ^ { \gamma } | 47babbb1-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_2.jpg |
\cos \alpha = \cos \alpha \prime - \epsilon \sin \alpha \prime | 1333f4de-bdf8-11e6-b796-001b63bd97ba__mathematical-expression-and-equation_8.jpg |
M = \frac { Q } { g } | 85c65cf0-7d1e-11e7-89ee-5ef3fc9ae867__mathematical-expression-and-equation_3.jpg |
v = M / ( E J ) | 4bc11c20-2ff3-4e61-a0f6-8572066d74a5__mathematical-expression-and-equation_0.jpg |
+ b _ { 1 0 } g _ { 1 0 } - b _ { 2 0 } g _ { 2 0 } = 0 , | 126ab771-40e4-11e1-1586-001143e3f55c__mathematical-expression-and-equation_4.jpg |
u ( 1 + v _ { 0 } - n _ { 0 } ) + \sum _ { t = 1 } ^ { T - 1 } \delta ^ { t } u ( 1 + \phi x _ { t - 1 } - \beta _ { t - 1 } - n _ { t } ) + \delta ^ { T } u ( 1 + \phi x _ { T - 1 } - \beta _ { T - 1 } ) | 397b7c50-dde0-4100-8957-d43c8c7388fa__mathematical-expression-and-equation_4.jpg |
\parallel \{ 2 ^ { k \bar { s } } T _ { 1 , k , l , j } \} ^ { \infty } _ { k = 0 } | L _ { \bar { p } } ( l _ { \infty } ) \parallel \le | 07df0bbb-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_8.jpg |
m = h ^ { 2 } + k ^ { 2 } | 9979c4d7-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_10.jpg |
\int _ { a } ^ { b } f ( x ) d x = [ F ( x ) + C ] _ { x = a } ^ { x = b } = | _ { a } ^ { b } F ( x ) = F ( b ) - F ( a ) . | 2f472600-63b1-11e3-bc9f-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg |
+ a + ( + b ) = + a + b = a + b | 43d24a3f-2259-11ea-8d84-001b63bd97ba__mathematical-expression-and-equation_2.jpg |
\frac { d F } { d x } = \frac { d F } { d r } \cdot \frac { x - u } { r } | 55fa6187-78ed-4a93-9b3f-eece7dba9cc3__mathematical-expression-and-equation_10.jpg |
a k = a ^ { 0 } k | 13ecb618-b6a3-49c9-9400-354084d77775__mathematical-expression-and-equation_4.jpg |
R ( x ) = \frac { \phi _ { 1 } ( x ) } { \Theta ^ { n } ( x ) } | 3a09a4c1-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_10.jpg |
\{ \begin{array} { c c c c c c } d _ { 1 } & u _ { \infty } & a _ { 1 } & i _ { 1 } & d _ { 1 } \prime & \dots \\ u _ { \infty } & e _ { 1 } & b _ { 1 } & j _ { 1 } & e _ { 1 } \prime & \dots \end{array} \} | 381e9d33-435e-11dd-b505-00145e5790ea__mathematical-expression-and-equation_1.jpg |
M ( x ^ { 2 } ) = \frac { 1 } { \pi h ( t ) \sqrt { D } } \int _ { - \infty } ^ { \infty } e ^ { - \frac { \alpha _ { 1 1 } n ^ { 2 } - 2 \alpha _ { 1 2 } u v + \alpha _ { 2 2 } v ^ { 2 } } { h ( t ) \cdot D } } | 99fcf451-c1f2-11eb-a5d1-001b63bd97ba__mathematical-expression-and-equation_18.jpg |
\delta _ { 4 } = 1 7 . | 971d9aa0-66bd-11e5-8a99-005056825209__mathematical-expression-and-equation_11.jpg |
\hat { \theta } = ( Z \prime M Z ) ^ { - 1 } Z \prime M y | 1998d614-12f7-4fae-b774-f75610f06b9c__mathematical-expression-and-equation_0.jpg |
u _ { 2 } = u _ { o } t - \frac { L } { E } \dot { u } _ { o } [ 1 - \exp ( - t / T ) ] | 9033ad82-b9f4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_3.jpg |
\angle a \prime b O = \angle a O b = \omega | 6f5a546d-f7ba-4ae1-95d4-b321b0e3cb97__mathematical-expression-and-equation_11.jpg |
\{ \begin{array} { c } \hat { x } ( t ) = - \sum _ { i = 1 } ^ { n ( t ) } \frac { x ( \tau ^ { - i } ( t ) ) } { H _ { i } ( \tau ^ { - i } ( t ) ) } - \frac { x ( T ) } { ( h ( \tau ^ { - 1 } ( T ) ) - 1 ) H _ { n ( t ) } ( \tau ^ { - n ( t ) } ( t ) ) } \\ \hat { x } ( t ) = - \frac { x ( T ) } { h ( \tau ^ { - 1 } ... | 08bd5e64-570b-11e1-7459-001143e3f55c__mathematical-expression-and-equation_3.jpg |
b _ { i } = \frac { 1 } { \pi } \int _ { 0 } ^ { 2 \pi } F ( x ) \sin i x d x | 0402f7cb-40e4-11e1-1418-001143e3f55c__mathematical-expression-and-equation_0.jpg |
( d a _ { 3 } + 3 a _ { 2 } \omega + \omega _ { 3 } ^ { 1 } ) \wedge | 07df0ba5-570b-11e1-5298-001143e3f55c__mathematical-expression-and-equation_26.jpg |
n \psi = n p = n p _ { 1 } | 0995825a-84ca-4375-afae-a7abf7ae47e9__mathematical-expression-and-equation_0.jpg |
L _ { 1 , 2 } = - 2 w _ { 1 , e } \frac { c h s \cos s + s h s \sin s } { s h 2 s - \sin 2 s } + \frac { 2 } { \kappa } w \prime _ { 1 , e } \frac { c h s s \in s } { s h 2 s - \sin 2 s } | 1138ecae-3c62-11e1-1586-001143e3f55c__mathematical-expression-and-equation_5.jpg |
\log \tan \sigma = 8 . 0 9 6 9 1 - 1 0 | 1bfc1901-8f46-4a7a-bda3-aab273016034__mathematical-expression-and-equation_2.jpg |
1 + \cot ^ { 2 } \phi = \csc ^ { 2 } \phi ; \frac { 1 } { \mathrm { s n } ^ { 2 } \phi } = 1 + \frac { A ^ { 2 } } { B ^ { 2 } } = \frac { A ^ { 2 } + B ^ { 2 } } { B ^ { 2 } } | 0b0fb410-3a1a-11e9-9fd6-5ef3fc9ae867__mathematical-expression-and-equation_7.jpg |
x \in C ^ { 0 } | 47babc56-f33d-11e1-1154-001143e3f55c__mathematical-expression-and-equation_11.jpg |
\frac { 1 } { \alpha _ { n } } \int _ { t _ { 1 } } ^ { t ^ { - } } U ( t ) ^ { n } d t = ( a + b s ) ^ { n } - ( a + b x ) ^ { n } | 0ecd6a43-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_4.jpg |
\bar { \omega } _ { p } ^ { ( 0 ) } = - \frac { a } { d } C _ { 5 } ^ { ( 0 ) } | 2051ac44-3c62-11e1-8486-001143e3f55c__mathematical-expression-and-equation_0.jpg |
P = ( 1 0 0 ) \infty P \infty ( | 06c84603-e3ab-11e6-a668-001999480be2__mathematical-expression-and-equation_4.jpg |
x = \tan ^ { 2 } \omega | 516592f3-54ad-4bf9-8449-e664af4df51d__mathematical-expression-and-equation_8.jpg |
\Delta D \prime _ { n } = D \prime _ { n } - \overline { D \prime } | 9b4b702e-e8e9-42e0-9032-2997791d50c4__mathematical-expression-and-equation_13.jpg |
5 , 8 \% P b _ { 3 } O _ { 4 } | 40171b16-df3d-11e1-1232-001143e3f55c__mathematical-expression-and-equation_1.jpg |
\sigma = \sum _ { i = 1 } ^ { i = n } \frac { K _ { i s } / h a } { K _ { i t } / h a } | 084e5960-b5b2-11ea-9c77-5ef3fc9ae867__mathematical-expression-and-equation_1.jpg |
h + \frac { \partial f ( x , y , z , \dots ) } { \partial y } . i + \frac { \partial f ( x , y , z , \dots ) } { \partial z } . k + \dots | 35aa05cc-b81c-4426-8f5b-7470441affa5__mathematical-expression-and-equation_11.jpg |
p ^ { 2 } + q r = ( p + q u ) ^ { 2 } | 0cc65872-5fe8-4adb-bf33-709dccb25d4c__mathematical-expression-and-equation_2.jpg |
\frac { u _ { 2 m - 1 } + u _ { 2 m } } { O _ { 2 m } ^ { 2 } } + \frac { u _ { 2 m } + u _ { 1 } } { O _ { 1 } ^ { 2 } } = - \frac { 1 } { 2 } | 079fa77b-40e4-11e1-8339-001143e3f55c__mathematical-expression-and-equation_13.jpg |
+ 2 \epsilon _ { 2 3 } ^ { 2 } [ 2 ( \epsilon _ { 2 2 } ^ { 2 } + \epsilon _ { 3 3 } ^ { 2 } ) + 3 \epsilon _ { 2 2 } \epsilon _ { 3 3 } - \epsilon _ { 1 1 } ^ { 2 } ] + 2 \epsilon _ { 3 1 } ^ { 2 } [ 2 ( \epsilon _ { 3 3 } ^ { 2 } + \epsilon _ { 1 1 } ^ { 2 } ) | 1cf70e88-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_10.jpg |
M g x _ { 0 } = m _ { 1 } g x _ { 1 } + m _ { 2 } g x _ { 2 } + \dots = | 208ff050-f0e4-11e2-9439-005056825209__mathematical-expression-and-equation_9.jpg |
\dots \mathbf { u } _ { S 3 } = \frac { 1 } { 3 } ( u _ { V } e ^ { j 2 / 3 \pi } + u _ { C 6 } e ^ { j \pi / 3 } ) = \frac { 1 } { 3 } [ u _ { V } e ^ { j 2 / 3 \pi } + ( u _ { C 4 } + u _ { C 5 } ) e ^ { j } | 5fb896c3-a5e9-4906-8c8d-8f3bc5faad91__mathematical-expression-and-equation_21.jpg |
\zeta = \zeta _ { 1 } + \zeta _ { 2 } + \zeta _ { 3 } + \dots | 959bd1a2-de39-4feb-a174-09bcacb166d7__mathematical-expression-and-equation_1.jpg |
3 = \frac { 5 \times 6 } { 1 0 } | 08326dca-e631-4952-9e6d-45f904520556__mathematical-expression-and-equation_5.jpg |
\frac { P + Q } { 2 } + \frac { 1 } { 2 } \sum _ { k = 1 } \frac { F ( r _ { 2 } ) - F ( r _ { 1 } ) } { k + 4 } ( r _ { 2 } ^ { k + 4 } - r _ { 1 } ^ { k + 4 } ) \binom { \frac { 1 } { 2 } } { \frac { k + 3 } { 2 } } | 30654e80-df3d-11e1-1287-001143e3f55c__mathematical-expression-and-equation_2.jpg |
\frac { D w } { D t } = \frac { \partial w } { \partial t } + u \frac { \partial w } { \partial x } + v \frac { \partial w } { \partial y } + w \frac { \partial w } { \partial z } = Z - \frac { 1 } { \rho } \frac { \partial p } { \partial z } | 1b3dee2f-3c62-11e1-7963-001143e3f55c__mathematical-expression-and-equation_4.jpg |
Z _ { 1 } - Z _ { 2 } = \pm 2 p | 1c1d5157-3c62-11e1-3052-001143e3f55c__mathematical-expression-and-equation_3.jpg |
\frac { r _ { j + 1 } - r _ { j } } { 2 } = \epsilon _ { j } \prime ; \frac { r _ { j + 2 } - r _ { j + 1 } } { 2 } = \epsilon _ { j } \prime \prime ; \dots ; \frac { r _ { j + j \prime } - r _ { j + j \prime - 1 } } { 2 } = \epsilon _ { j } ^ { ( j \prime ) } | 3f277f55-408b-11e1-8339-001143e3f55c__mathematical-expression-and-equation_3.jpg |
Q \prime _ { \mu } = Q _ { \mu } - \frac { \partial \log F } { \partial \xi ^ { \mu } } | 0e4660e2-40e4-11e1-1121-001143e3f55c__mathematical-expression-and-equation_3.jpg |
Y = - 0 . 3 + 0 . 2 0 0 X | 2a55dc88-4ce4-11e1-1726-001143e3f55c__mathematical-expression-and-equation_8.jpg |
\sphericalangle m c b + c b m = R , | 17a619d0-e929-11e4-a794-5ef3fc9bb22f__mathematical-expression-and-equation_2.jpg |
\frac { \partial p _ { 0 } } { \partial t } = - p _ { 0 } \frac { \partial c } { \partial s } | 43b6a980-d866-4b84-97b9-407007e64205__mathematical-expression-and-equation_2.jpg |
\frac { v d v } { e ^ { - \frac { v } { 2 5 } } | 1 - e ^ { \frac { v } { 2 5 } } ( 0 . 0 0 4 5 - 0 . 0 0 0 0 7 1 5 v ^ { 2 } ) | } = - 0 . 1 g d \lambda | 3b1cc537-dbba-11e6-8be1-001b63bd97ba__mathematical-expression-and-equation_1.jpg |
\Sigma \frac { 1 } { \cos ^ { 3 } \alpha } = 2 \times 1 9 . 5 1 4 | 2574b750-31e7-11e4-90aa-005056825209__mathematical-expression-and-equation_5.jpg |
= \hat { 2 } < E _ { p } \frac { \tau _ { p } } { \mu _ { p } } \sum _ { k = \alpha , \beta } \kappa _ { k } [ 1 - \frac { \mu _ { k } } { \mu _ { p } } \ln ( 1 + \frac { \mu _ { p } } { \mu _ { k } } ) ] | 9a4ea058-4334-11e1-1589-001143e3f55c__mathematical-expression-and-equation_0.jpg |
x _ { 0 } ^ { 2 } + y _ { 0 } ^ { 2 } = ( 2 r ) ^ { 2 } | 8e512500-7ad7-11e8-9690-005056827e51__mathematical-expression-and-equation_6.jpg |
\frac { 1 5 } { 2 2 } : 1 7 \frac { 1 } { 4 } = x . | 05fd0c1d-224c-11ea-bbb4-001b63bd97ba__mathematical-expression-and-equation_13.jpg |
x = \frac { a + b } { 2 } | 39dda871-c060-11e6-855e-001b63bd97ba__mathematical-expression-and-equation_3.jpg |
> 1 - \lambda , | 02b32dd6-ac0b-11e1-1589-001143e3f55c__mathematical-expression-and-equation_15.jpg |
V = \frac { B ( v + x ) } { 3 } - \frac { b x } { 3 } = \frac { B v } { 3 } + \frac { x } { 3 } ( B - b | 4cce0e06-2dac-11ec-b355-001b63bd97ba__mathematical-expression-and-equation_2.jpg |
\parallel \kappa _ { 3 , 0 } + p \kappa _ { 3 , 1 } + p ^ { 2 } \kappa _ { 3 , 2 } \dots + , \kappa _ { 4 , 0 } + p \kappa _ { 4 , 1 } + p ^ { 2 } \kappa _ { 4 , 2 } + \dots | 11f9f260-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_11.jpg |
P = P ( t ) > 0 | 5841cd7d-be8f-491c-adb3-1a631f6252fd__mathematical-expression-and-equation_11.jpg |
1 a + 1 6 b ( a + b ) ( 6 a + 1 1 b ) - 4 ( 3 a + 4 b ) ( 4 a + 5 b ) ( a + 2 b ) = | 3790b91e-eb13-11ec-b47a-00155d01210b__mathematical-expression-and-equation_29.jpg |
= 1 + \frac { 1 } { n } \sum _ { \lambda = 2 , 4 , \dots } ^ { \infty } \frac { ( - 1 ) ^ { \frac { \lambda } { 2 } } } { ( \lambda + 1 ) ! } ( \frac { 2 m \pi } { n } ) ^ { \lambda } \mathbf { B } _ { \lambda - 1 } ( n ) \dots | 324aafa8-df3d-11e1-1027-001143e3f55c__mathematical-expression-and-equation_3.jpg |
I \prime = V \prime Y \prime | 11f9f2c4-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_7.jpg |
f ( a , t ) = \sum _ { i = 1 } ^ { N } a _ { i } \phi _ { i } ( t ) | 0ecd6a07-3c62-11e1-8339-001143e3f55c__mathematical-expression-and-equation_1.jpg |
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