Returned 94 matches (100 formulae, 76 docs)
    Lookup 622.275 ms, Re-ranking 1530.751 ms
    Found 1639172 tuple postings, 191749 formulae, 21922 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 )

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

0.2595
-14.0000
4.0000
p = 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 y ) ( 1 x )
( 1 x ) ( 1 y )

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

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 ( Δ ) V ) x ( N B ( Δ ) V ) y
K s p = ( N A ( f ) V ) x ( N B ( f ) 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
B n 1 n ( n W ( n ) ) n + 1 2 exp ( n W ( n ) - n - 1 ) .

0.1818
-22.0000
3.0000
S 2 - 1.5382 Γ ( 3 2 ) 2 ( Γ ( 5 2 ) - Γ ( 3 2 ) ) 0.0854

0.1681
-7.0000
3.0000
tan ( arccsc x ) = 1 x 2 - 1

0.1681
-7.0000
3.0000
sin ( arcsec x ) = x 2 - 1 x
cos ( arccsc x ) = x 2 - 1 x

0.1681
-7.0000
3.0000
( arcosh x ) = 1 x 2 - 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
-20.0000
3.0000
j 2 ( x ) = ( 3 x 2 - 1 ) sin ( x ) x - 3 cos ( x ) x 2

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

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
f = v 2 ( L x ) 2 + ( m L y ) 2 + ( n L z ) 2

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

0.1422
-10.0000
2.0000
( δ - ( λ d ) 1 - ( λ d ) ) 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
-14.0000
3.0000
P ( x ) ( 1 - x ) ( 1 - x 2 ) ( 1 - x n )

0.1422
-16.0000
3.0000
P 4 2 ( x ) = 15 2 ( 7 x 2 - 1 ) ( 1 - x 2 )

0.1422
-16.0000
3.0000
( d y d x ) 2 = ( y 2 - 1 ) ( 1 - k 2 - y 2 )

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

0.1422
-20.0000
2.0000
f ( x ) = 1 2 1 2 Γ ( 1 2 ) x - 1 2 e - x 2

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

0.1422
-21.0000
2.0000
θ = arctan ( x 2 + y 2 z ) = arccos ( z x 2 + y 2 + z 2 )

0.1422
-22.0000
2.0000
F ( x ) = Φ ( x - μ σ ) = 1 2 [ 1 + erf ( x - μ σ 2 ) ]

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

0.1422
-23.0000
3.0000
σ y y = μ b 2 π ( 1 - ν ) y ( x 2 - y 2 ) ( x 2 + y 2 ) 2
τ x y = μ b 2 π ( 1 - ν ) x ( x 2 - y 2 ) ( x 2 + y 2 ) 2

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

0.1422
-30.0000
2.0000
4 0 1 ( x 2 - x 6 ) 1 6 d x = Γ ( 1 6 ) Γ ( 1 3 ) 3 π 2.804 ,

0.1297
-9.0000
3.0000
V = 1 2 ( x 1 2 + x 2 2 )

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

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

0.1297
-13.0000
2.0000
j 1 ( x ) = sin ( x ) x 2 - cos ( x ) x

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

0.1297
-14.0000
3.0000
T = 1 2 x ˙ 2 = 1 2 ( x t ) 2

0.1297
-14.0000
3.0000
R 2 ( x ) = x 2 - 4 x + 1 ( x + 1 ) 2

0.1297
-14.0000
2.0000
e 𝛀 θ 2 = cos ( θ 2 ) + 𝛀 sin ( θ 2 )

0.1297
-14.0000
2.0000
K ( 2 2 ) = 1 4 π Γ ( 1 4 ) 2

0.1297
-14.0000
2.0000
K n ( x ) = ( x 2 ) n 𝒦 n ( x 2 4 ) .

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

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

0.1297
-17.0000
2.0000
a 2 = 2 x - 2 x - 2 x 2 - 2 x + 3 2

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

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

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

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

0.1297
-20.0000
2.0000
Φ ( k + 1 ) ( ω ) = 1 2 H ( ω 2 ) Φ ( k ) ( ω 2 )

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

0.1297
-20.0000
2.0000
f ( x ) = 2 ω ϕ ( x - ξ ω ) Φ ( α ( x - ξ ω ) ) .

0.1297
-21.0000
2.0000
= ( 1 2 ( t j - y j ) 2 ) y j y j w j i

0.1297
-22.0000
3.0000
= 1 θ k Γ ( k ) ( 1 y ) k - 1 exp ( - 1 θ y ) 1 y 2

0.1297
-23.0000
2.0000
f ( x ) = 1 2 k / 2 Γ ( k / 2 ) x k 2 - 1 exp ( - x 2 )

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
-24.0000
2.0000
f ( x ) = 1 2 n ( x - y | x - y | + y | y | ) d μ ( y )

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

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

0.1297
-28.0000
2.0000
v a r [ log ( t a ) ] = ( s a 2 t a 2 + ( x a - x ¯ t a ) 2 - 1 ) n

0.1087
-12.0000
2.0000
f ( x ) = 1 ( x - 1 ) ( x 2 + x + 1 )

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

0.1013
-9.0000
2.0000
1 - ( x x i ) k x - x i

0.1013
-11.0000
2.0000
r x y = x y ¯ ( x 2 ¯ ) ( y 2 ¯ )

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

0.1013
-14.0000
1.0000
f ( i ) i = 1 2 + O ( log log i i )

0.1013
-17.0000
3.0000
v = x - x ¯ h ( x ) ; w = y - y ¯ h ( y )

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

0.1013
-22.0000
3.0000
( 1 + 2 x ) ( 1 + 5 x - 16 x 4 ) ( 1 - x 2 ) ( 1 - 16 x 2 )

0.1013
-22.0000
2.0000
d ( d ( d y d x ) d x ) d x = ( d d x ) 3 ( f ( x ) )

0.0909
-14.0000
1.0000
b 3 = 3 y 2 - y 1 ( x 2 - x 1 ) 2

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

0.0909
-17.0000
1.0000
1 ( R - x ) 2 + 1 ( R + x ) 2 = 1 r 2

0.0909
-19.0000
1.0000
r = z ( 1 + ( x - x ) 2 + y 2 z 2 ) 1 2

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

0.0909
-19.0000
1.0000
r z ( 1 + 1 2 ( x - x ) 2 + y 2 z 2 )

0.0909
-21.0000
2.0000
f y = y 0 - y ( x 0 - x ) 2 + ( y 0 - y ) 2 ( 20 )
f x = x 0 - x ( x 0 - x ) 2 + ( y 0 - y ) 2 ( 19 )

0.0909
-21.0000
2.0000
F ( x ) = 2 π arcsin ( x ) = arcsin ( 2 x - 1 ) π + 1 2

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

0.0909
-23.0000
3.0000
f ( x ) = 2 2 k / 2 Γ ( k / 2 ) x k - 1 exp ( - x 2 2 )