Returned 95 matches (100 formulae, 74 docs)
    Lookup 735.734 ms, Re-ranking 1489.674 ms
    Found 1759181 tuple postings, 216911 formulae, 22624 documents
[ formulas ] [ documents ] [ documents-by-formula ]

0.9245
-16.0000
22.0000
p = - x ± x 2 - 4 ( - g x 2 2 v 2 ) ( - g x 2 2 v 2 - y ) 2 ( - g x 2 2 v 2 )

0.4660
-55.0000
12.0000
x = - b ± b 2 - 4 a c 2 a x = y 2 y 1 = - 1 2 ± 1 2 2 - 4 ( 1 2 ) ( - F r 1 2 ) 2 ( 1 2 ) = - 1 2 ± 1 4 + 2 F r 1 2 1

0.2979
-12.0000
4.0000
f ′′ ( x ) = ( q p ) ( q p - 1 ) x q p - 2

0.2821
-7.0000
4.0000
R i - ( 1 + i ) n ( R i - P )

0.2595
-14.0000
4.0000
p = v 2 ± v 4 - g ( g x 2 + 2 y v 2 ) g x

0.2595
-15.0000
4.0000
tan θ = v 2 ± v 4 - g ( g x 2 + 2 y v 2 ) g x

0.2595
-16.0000
4.0000
θ = arctan ( v 2 ± v 4 - g ( g x 2 + 2 y v 2 ) g x )

0.2595
-18.0000
4.0000
θ = tan - 1 ( v 2 ± v 4 - g ( g x 2 + 2 y v 2 ) g x )

0.2595
-26.0000
4.0000
z = 1 2 ( x 2 + y 2 ) ( 1 a 2 - 1 b 2 ) + x y ( 1 a 2 + 1 b 2 )

0.2062
-2.0000
3.0000
( 1 x ) ( 1 y )
( 1 y ) ( 1 x )

0.2062
-6.0000
3.0000
( p + r 2 ) ( q + s 2 )

0.2062
-7.0000
3.0000
( p - 1 2 ) ( q - 1 2 ) ,

0.2062
-7.0000
3.0000
= ( 3 331 ) ( 5 331 ) ( 823 331 )
= ( 3 331 ) ( 5 331 ) ( 161 331 )

0.2062
-8.0000
3.0000
( a m n ) = ( a m ) ( a n )
( a n m ) = ( a n ) ( a m )

0.2062
-8.0000
3.0000
( a b n ) = ( a n ) ( b n )

0.2062
-11.0000
4.0000
( v c ) 2 ( r r s - 1 ) = 1 2 .

0.2062
-11.0000
3.0000
= ( 3 331 ) ( 5 331 ) ( 7 331 ) ( 23 331 )

0.2062
-11.0000
3.0000
( α 𝔭 ) n ( β 𝔭 ) n = ( α β 𝔭 ) n

0.2062
-12.0000
3.0000
log ( G ( 1 2 + z ) G ( 1 2 - z ) ) =

0.2062
-14.0000
4.0000
D 1 = ( h 1 - 1 γ ) ( 1 h 1 - 1 h 2 )

0.2062
-14.0000
3.0000
K s p = ( N A ( f ) V ) x ( N B ( f ) V ) y
K s p = ( N A ( Δ ) V ) x ( N B ( Δ ) V ) y

0.2062
-19.0000
5.0000
0 = - g x 2 2 v 2 p 2 + x p - g x 2 2 v 2 - y

0.2062
-21.0000
5.0000
0 = - g x 2 2 v 2 tan 2 θ + x tan θ - g x 2 2 v 2 - y

0.2062
-24.0000
4.0000
σ x x = - μ b 2 π ( 1 - ν ) y ( 3 x 2 + y 2 ) ( x 2 + y 2 ) 2

0.2062
-24.0000
3.0000
F ( ε ) = ε 2 0 1 ( 2 u - ln ( 1 u ) - 2 ) e - ε u d u

0.2062
-24.0000
3.0000
B n 1 n ( n W ( n ) ) n + 1 2 exp ( n W ( n ) - n - 1 ) .

0.1931
-16.0000
5.0000
ζ Ai ( 1 ) = - 3 - 2 / 3 Γ ( 2 3 ) Γ ( 4 3 ) .

0.1818
-9.0000
2.0000
v 1 ( 1 2 ) = v 2 ( 1 2 )

0.1818
-11.0000
4.0000
μ λ = sin ( A + D λ 2 ) sin ( A 2 )

0.1818
-26.0000
4.0000
ϕ ( p ) = ( x 0 π ) 1 / 2 exp ( - x 0 2 ( p - p 0 ) 2 2 2 ) ,

0.1681
-10.0000
3.0000
- ( T V ) P ( S P ) V

0.1681
-11.0000
3.0000
( z x ) y ( x z ) y = 1.

0.1681
-11.0000
3.0000
= 2 ( t a - floor ( 1 2 + t a ) )

0.1681
-18.0000
3.0000
( z x ) y = - ( z y ) x ( y x ) z

0.1681
-19.0000
3.0000
( x y ) z ( y z ) x ( z x ) y = - 1

0.1681
-19.0000
3.0000
( z x ) y ( x y ) z = - ( z y ) x .

0.1681
-20.0000
3.0000
( 8 )    ( z y ) x = - ( z x ) y ( x y ) z

0.1681
-21.0000
3.0000
q 2 g ( 1 y 1 - 1 y 2 ) = 1 2 ( y 2 2 - y 1 2 )
q 2 g ( 1 y 1 - 1 y 2 ) = 1 2 ( y z 2 - y 1 2 )

0.1681
-21.0000
3.0000
| x - 1 2 ( a c + b d ) | = 1 2 ( b d - a c )

0.1681
-22.0000
3.0000
1 ( u + A ) ( u - A ) = 1 2 A ( 1 u - A - 1 u + A )

0.1681
-29.0000
3.0000
E I d 4 w d x 4 - 3 2 E A ( d w d x ) 2 ( d 2 w d x 2 ) = q ( x )

0.1519
-19.0000
4.0000
f ( x ) = 2 β α 2 Γ ( α 2 ) x α - 1 exp ( - β x 2 )

0.1519
-20.0000
4.0000
r x y = x y ¯ - x ¯ y ¯ ( x 2 ¯ - x ¯ 2 ) ( y 2 ¯ - y ¯ 2 )

0.1519
-20.0000
3.0000
w = i ( x i - x ¯ ) ( d i - d ¯ ) i ( x i - x ¯ ) 2

0.1519
-20.0000
3.0000
f = v 2 ( L x ) 2 + ( m L y ) 2 + ( n L z ) 2

0.1519
-21.0000
1.0000
S 2 = 2 m [ m ( 2 ) - x ¯ 2 2 x ¯ ] 2 = m ( d ~ - 1 ) 2 2

0.1519
-22.0000
5.0000
f ( x ; k ) = 2 1 - k 2 x k - 1 e - x 2 2 Γ ( k 2 )

0.1519
-24.0000
4.0000
2 π ε l arcosh ( d a ) = 2 π ε l ln ( d a + d 2 a 2 - 1 )

0.1422
-8.0000
2.0000
v 1 ( 1 2 ) = v 2 ( 1 2 )

0.1422
-12.0000
2.0000
S N ( f ) = N 0 2 ( 1 + ( w B ) 2 )

0.1422
-13.0000
3.0000
tan A = ( ( - z y ) ( z x ) )

0.1422
-14.0000
3.0000
d y d x = - 4 x 3 4 y = - x 3 y

0.1422
-17.0000
2.0000
Q = 2 N 2 N - 1 = 1 2 sinh ( ln ( 2 ) 2 N )

0.1422
-18.0000
4.0000
( x 2 2 + y x ) d y = y x 2 2 + x y 2 2

0.1422
-21.0000
2.0000
( 1 2 ( x - 1 x ) ) 2 + 1 = ( 1 2 ( x + 1 x ) ) 2 ,

0.1422
-23.0000
4.0000
d d x ( 1 x 3 + 4 x ) = - 3 x 2 - 4 ( x 3 + 4 x ) 2 .

0.1422
-23.0000
3.0000
Q ( x ) = 1 2 - 1 2 erf ( x 2 ) = 1 2 erfc ( x 2 ) .

0.1422
-24.0000
2.0000
ϕ = arctan ( y x ) = arccos ( x x 2 + y 2 ) = arcsin ( y x 2 + y 2 )

0.1297
-7.0000
3.0000
1 2 ( x 2 - 4 x + 2 )

0.1297
-12.0000
4.0000
f ( x ) = x 3 - 2 x 2 ( x 2 - 5 )

0.1297
-12.0000
2.0000
sin ( x 2 ) = ± 1 2 ( 1 - cos x )

0.1297
-13.0000
2.0000
ϕ = tan - 1 ( y 1 - y 2 x 1 - x 2 )

0.1297
-14.0000
3.0000
η p = 2 ( v v e ) 1 + ( v v e ) 2

0.1297
-14.0000
3.0000
X = 1 2 [ ( T β ) 0.5 - ( T β ) - 0.5 ]

0.1297
-14.0000
2.0000
haversin ( θ ) = sin 2 ( θ 2 ) = 1 - cos ( θ ) 2

0.1297
-16.0000
2.0000
r r s ( v c ) 2 ( 1 - r s r ) = 1 2

0.1297
-16.0000
2.0000
( J 0 3 f ) ( x ) = - x - x 2 2 - x 3 3

0.1297
-17.0000
3.0000
ω ± = ω c 2 ± ( ω c 2 ) 2 - ω t 2 2

0.1297
-17.0000
3.0000
e = ( x 0 - x ) 2 + ( y 0 - y ) 2 2 a ( 17 )

0.1297
-17.0000
3.0000
f ( x ) = 1 + 2 ( 1 x + x x 2 - 4 x + 8 )

0.1297
-18.0000
3.0000
= 1 θ k Γ ( k ) ( 1 y ) k + 1 exp ( - 1 θ y )

0.1297
-18.0000
3.0000
d d x ( 1 g ( x ) ) = - g ( x ) ( g ( x ) ) 2

0.1297
-18.0000
3.0000
y = R ( 2 ( x L ) - K ( x L ) 2 2 - K )

0.1297
-18.0000
2.0000
[ cos ( θ 2 ) - sin ( θ 2 ) sin ( θ 2 ) cos ( θ 2 ) ]

0.1297
-19.0000
2.0000
K = 2 ( Γ ( n - 1 2 ) ) 2 ( Γ ( n - 2 2 ) ) 2 .

0.1297
-19.0000
2.0000
d d x ( 1 g ( x ) ) = d d x ( f ( x ) g ( x ) )

0.1297
-20.0000
3.0000
1 +  2 ( 1 8 ) +  4 ( 1 8 ) 2 +  8 ( 1 8 ) 3 + .

0.1297
-20.0000
3.0000
1 + 7 x + 12 x 2 - 4 x 3 ( 1 - x 2 ) ( 1 - 16 x 2 )

0.1297
-20.0000
2.0000
K = 2 ( Γ ( N - t 2 ) ) 2 ( Γ ( N - t - 1 2 ) ) 2

0.1297
-21.0000
3.0000
ln ( p ( z 2 ) p ( z 1 ) ) = - g R T ¯ ( z 2 - z 1 )

0.1297
-24.0000
2.0000
θ = tan - 1 ( ( x 1 - x 2 ) 2 + ( y 1 - y 2 ) 2 z 1 - z 2 )

0.1297
-26.0000
3.0000
π x 2 6 - 3 x 2 - ( x 2 ) 2 2 + x 2 - ( x 2 ) 2 2

0.1297
-26.0000
3.0000
0 x n e - a x 2 d x = Γ ( ( n + 1 ) 2 ) 2 a ( n + 1 ) 2

0.1087
-22.0000
4.0000
α ( x ) = x + x 2 + 4 2 ,  β ( x ) = x - x 2 + 4 2

0.1013
-12.0000
3.0000
1 + 7 x ( 1 - x 2 ) ( 1 - 16 x 2 )

0.1013
-12.0000
2.0000
( d x d t ) 2 + ( d y d t ) 2

0.1013
-14.0000
2.0000
( z x ) y = 1 ( x z ) y .

0.1013
-20.0000
3.0000
p = g z ( g x ) 2 + ( g y ) 2

0.1013
-20.0000
2.0000
( x y ) z = - ( z y ) x ( z x ) y

0.1013
-20.0000
2.0000
1 r = ( d 2 x d s 2 ) 2 + ( d 2 y d s 2 ) 2

0.1013
-26.0000
2.0000
A y = 2 π a b x ( t ) ( d x d t ) 2 + ( d y d t ) 2 d t ,

0.0909
-16.0000
2.0000
d ( d ( d ( f ( x ) ) d x ) d x ) d x ,

0.0909
-19.0000
1.0000
x ( 2 x 2 + y 2 ) y ( a 2 - x 2 ) = d y d x

0.0909
-21.0000
2.0000
d s 2 = 4 ( d x 2 + d y 2 ) ( 1 - x 2 - y 2 ) 2 .

0.0909
-21.0000
2.0000
f y = y 0 - y ( x 0 - x ) 2 + ( y 0 - y ) 2 ( 20 )