Returned 98 matches (100 formulae, 57 docs)
    Lookup 677.030 ms, Re-ranking 10591.975 ms
    Found 1235439 tuple postings, 220790 formulae, 22789 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
0.9733
-19.0000
31.0000
6.9308
testing/wikipedia/v3/14488.html
| Ψ > = i 1 , i 2 , α 1 , α 2 Γ α 1 [ 1 ] i 1 λ α 1 [ 1 ] Γ α 1 α 2 [ 2 ] i 2 λ α 2 [ 2 ] | i 1 i 2 > | Φ α 2 [ 3.. N ] >
c i 1 i 2 . . i N = α 1 , . . , α N - 1 = 0 χ Γ α 1 [ 1 ] i 1 λ α 1 [ 1 ] Γ α 1 α 2 [ 2 ] i 2 λ α 2 [ 2 ] Γ α 2 α 3 [ 3 ] i 3 λ α 3 [ 3 ] . . Γ α N - 2 α N - 1 [ N - 1 ] i N - 1 λ α N - 1 [ N - 1 ] Γ α N - 1 [ N ] i N
| Ψ > = i 1 , α 1 = 1 M , χ Γ α 1 [ 1 ] i 1 λ α 1 [ 1 ] | i 1 > | Φ α 1 [ 2.. N ] >
| ψ > = α , β , γ = 1 χ i , j = 1 M λ α [ C - 1 ] Γ α β [ C ] i λ β [ C ] Γ β γ [ D ] j λ γ [ D ] | α i j γ >
| Φ α k [ 1.. k ] = α 1 , α 2 . . α k - 1 Γ α 1 [ 1 ] i 1 λ α 1 [ 1 ] Γ α k - 1 α k [ k ] i k | i 1 i 2 . . i k
| τ α 1 i 2 [ 3.. N ] > = α 2 Γ α 1 α 2 [ 2 ] i 2 λ α 2 [ 2 ] | Φ α 2 [ 3.. N ] >
| Φ [ J C ] > = i , α Γ α β [ C ] i λ α | α i > .
| Φ [ D K ] > = j , γ Γ β γ [ D ] j λ γ | j γ > .
| Ψ > = α k λ α k [ k ] | Φ α k [ 1.. k ] > | Φ α k [ k + 1.. N ] >
| Φ α k [ k + 1.. N ] = α k + 1 , α k + 2 . . α N Γ α k α k + 1 [ k + 1 ] i k + 1 λ α k + 1 [ k + 1 ] λ α N - 1 N - 1 Γ α N - 1 [ N ] i N | i k + 1 i k + 2 . . i N
λ β | Φ β [ J C ] > = < Φ β [ D K ] | ψ > = i , j , α , γ ( Γ β γ [ D ] j ) * Θ α γ i j ( λ γ ) 2 λ α | α i >
| Φ α 1 [ 2.. N ] > = i 2 | i 2 > | τ α 1 i 2 [ 3.. N ] >
| Ψ > = i = 1 M a i | Φ i A Φ i B >
| ψ D > = 1 ϵ n α n = χ c χ λ α n [ n ] | Φ α n [ 1.. n ] > | Φ α n [ n + 1.. N ] >
| ψ D > = 1 1 - ϵ n α n = 1 χ c λ α n [ n ] | Φ α n [ 1.. n ] > | Φ α n [ n + 1.. N ] >
| Ψ > = 1 α l = 1 χ c | λ α l [ l ] | 2 α l = 1 χ c λ α l [ l ] | Φ α l [ 1.. l ] > | Φ α l [ l + 1.. N ] > ,
| Ψ > = 3 + 1 2 2 | ϕ 1 A ϕ 1 B > + 3 - 1 2 2 | ϕ 2 A ϕ 2 B >
Γ α k - 1 α k [ k ] i k = j U j k i k Γ α k - 1 α k [ k ] j k .
( c α l - 1 α l ) 2 = i l = 1 d ( Γ α l - 1 α l [ l ] i l ) * Γ α l - 1 α l [ l ] i l
| Ψ = i = 1 M c i 1 i 2 . . i N | i 1 , i 2 , . . , i N - 1 , i N
ρ [ 1.. k - 1 ] = α ( λ α [ k - 1 ] ) 2 | Φ α [ 1.. k - 1 ] > < Φ α [ 1.. k - 1 ] | = α ( λ α [ k - 1 ] ) 2 | α > < α | .
| Φ α 1 [ 1 ] > | Φ α 1 [ 2.. N ] >
n 1 = 1 = α l = 1 χ c ( c α l - 1 α l ) 2 ( λ α l [ l ] ) 2 + α l = χ c χ ( c α l - 1 α l ) 2 ( λ α l [ l ] ) 2 = S 1 + S 2
n 2 = α l = 1 χ c ( c α l - 1 α l ) 2 ( λ α l [ l ] ) 2 = α l = 1 χ c ( c α l - 1 α l ) 2 ( λ α l [ l ] ) 2 R = S 1 R
Doc 2
0.6125
-103.0000
19.0000
0.7684
testing/wikipedia/v3/23408.html
| Ψ = i 1 , . . , i N = 1 M α 1 , . . , α N - 1 = 0 χ Γ α 1 [ 1 ] i 1 λ α 1 [ 1 ] Γ α 1 α 2 [ 2 ] i 2 λ α 2 [ 2 ] Γ α 2 α 3 [ 3 ] i 3 λ α 3 [ 3 ] . . Γ α N - 2 α N - 1 [ N - 1 ] i N - 1 λ α N - 1 [ N - 1 ] Γ α N - 1 [ N ] i N | i 1 , i 2 , . . , i N - 1 , i N
Γ α l - 1 α l [ l ] i l , l = 1 , 2 k - 1

Doc 3
0.2436
-24.0000
5.0000
0.2436
testing/wikipedia/v3/08738.html
| s , m > = m 1 + m 2 = m C m 1 m 2 m s 1 s 2 s | s 1 m 1 > | s 2 m 2 >

Doc 4
0.2201
-30.0000
2.0000
0.4344
testing/wikipedia/v3/16662.html
h k ( X 1 , X 2 , , X n ) = 1 i 1 i 2 i k n X i 1 X i 2 X i k .
h k ( X 1 , X 2 , , X n ) = 1 i 1 , i 2 , , i k n m 1 ! m 2 ! m n ! k ! X i 1 X i 2 X i k ,

Doc 5
0.2104
-22.0000
2.0000
0.3828
testing/wikipedia/v3/26127.html
M α = i 1 < i 2 < < i k x i 1 α 1 x i 2 α 2 x i k α k .
x i 1 α 1 x i 2 α 2 x i k α k

Doc 6
0.2079
-32.0000
5.0000
0.2079
testing/wikipedia/v3/21860.html
| Ψ A 1 A m > = i = 1 m i n { d A 1 , , d A m } a i | e A 1 i > | e A m i >

Doc 7
0.2007
-18.0000
6.0000
0.2007
testing/wikipedia/v3/26485.html
| Ψ > = { s } Tr [ A s 1 A s 2 A s N ] | s 1 s 2 s N >

Doc 8
0.2007
-36.0000
3.0000
0.2007
testing/wikipedia/v3/13559.html
Ψ ω = α 1 , , α G A ω , α G G A α G , α G - 1 G - 1 A α 3 , α 2 2 A α 2 , α 1 1 x α 1

Doc 9
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0.0000
0.1993
testing/wikipedia/v3/02255.html
a i 1 i 2 a i 2 i 3 a i k i 1 = a i 2 i 1 a i 3 i 2 a i 1 i k

Doc 10
0.1937
-52.0000
6.0000
0.1937
testing/wikipedia/v3/03194.html
< Ψ n | Ψ n > ν = lim M i 1 , i n , j 1 , j n < M a i 1 , , i n * a j 1 , , j n < ψ i 1 | ψ j 1 > < ψ i n | ψ j n >

Doc 11
0.1925
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6.0000
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testing/wikipedia/v3/12144.html
| ψ > = i λ i | i A > | i B >
| ϕ > = i λ i | i A > | i B >

Doc 12
0.1925
-15.0000
1.0000
0.5316
testing/wikipedia/v3/24253.html
T = T i 1 i 2 i k e i 1 e i 2 e i k ,
T = i 1 , , i k = 1 N T i 1 i 2 i k e i 1 e i 2 e i k
Sym T = 1 k ! σ 𝔖 k T i σ 1 i σ 2 i σ k e i 1 e i 2 e i k .
Doc 13
0.1925
-20.0000
3.0000
0.3850
testing/wikipedia/v3/00996.html
α ω = i 1 < i 2 < < i p a i 1 i p w i 1 w i p ω .
α = i 1 < i 2 < < i p a i 1 i p w i 1 w i p + j B j w j

Doc 14
0.1925
-21.0000
3.0000
0.1925
testing/wikipedia/v3/02918.html
ψ ( x 1 , , x n ) = i 1 i ψ i 1 i x i 1 x i .

Doc 15
0.1786
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2.0000
0.3214
testing/wikipedia/v3/17173.html
g i 1 j 1 g i 2 j 2 g i n j n A i 1 i 2 i n = A j 1 j 2 j n
g i 1 j 1 g i 2 j 2 g i n j n A i 1 i 2 i n = A j 1 j 2 j n

Doc 16
0.1725
-10.0000
2.0000
0.1725
testing/wikipedia/v3/15599.html
c x 1 [ i 1 ] x 2 [ i 2 ] x n [ i n ]

Doc 17
0.1721
-23.0000
2.0000
0.1721
testing/wikipedia/v3/23240.html
a i 1 , i 2 = j 1 j 2 s j 1 , j 2 u i 1 , j 1 v i 2 , j 2 .

Doc 18
0.1646
-19.0000
2.0000
0.1646
testing/wikipedia/v3/02357.html
H = - i 1 < i 2 < < i r J i 1 i r S i 1 S i r

Doc 19
0.1646
-33.0000
1.0000
0.3205
testing/wikipedia/v3/09402.html
𝐞 i 1 i 2 i p j 1 j 2 j q = 𝐞 i 1 𝐞 i 2 𝐞 i p 𝐞 j 1 𝐞 j 2 𝐞 j q
S ¯ j 1 j 2 j p = det ( L ) 𝖫 i 1 j 1 𝖫 i 2 j 2 𝖫 i p j p S i 1 i 2 i p .

Doc 20
0.1559
-15.0000
1.0000
0.4108
testing/wikipedia/v3/07013.html
v i α , v i 1 i 2 α , , v i 1 i 2 i r α
+ V i 1 i 2 α ( x , u , w ) w i 1 i 2 α + + + V i 1 i 2 i r α ( x , u , w ) w i 1 i 2 i r α
( x , u , w , v i α , v i 1 i 2 α , , v i 1 i 2 i r α )
Doc 21
0.1559
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0.0000
0.1559
testing/wikipedia/v3/01446.html
e i 1 e i 2 e i k e i 1 e i 2 e i k .

Doc 22
0.1559
-28.0000
2.0000
0.1559
testing/wikipedia/v3/02847.html
i 1 , i 2 , ε i 1 i n a i 1 j 1 a i n j n = det ( 𝐀 ) ε j 1 j n

Doc 23
0.1559
-29.0000
1.0000
0.1559
testing/wikipedia/v3/03102.html
i 1 , i 2 i k = 1 n f i 1 i 2 i k d x i 1 d x i 2 d x i k

Doc 24
0.1559
-35.0000
1.0000
0.1559
testing/wikipedia/v3/05196.html
i 1 , i 2 , , i k { 1 , 2 , , n } a i 1 , i 2 , , i k X i 1 X i 2 X i k ,

Doc 25
0.1485
-28.0000
0.0000
0.1485
testing/wikipedia/v3/08448.html
R = c s 1 i n - i n - 1 s 2 i n - 1 - i n - 2 s n - 1 i 2 - i 1 s n i 1

Doc 26
0.1429
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4.0000
0.1429
testing/wikipedia/v3/00874.html
| ψ > A = i c i A | i > A

Doc 27
0.1429
-29.0000
2.0000
0.1429
testing/wikipedia/v3/14094.html
A ( α ) = - k , j s Ric j ¯ α k ¯ α i 1 i 2 i p j ¯ 1 j ¯ 2 k ¯ j ¯ q

Doc 28
0.1363
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1.0000
0.1720
testing/wikipedia/v3/05791.html
x α = x 1 α 1 x 2 α 2 x n α n
α = 1 α 1 2 α 2 n α n

Doc 29
0.1363
-18.0000
1.0000
0.1363
testing/wikipedia/v3/00410.html
n = p 1 α 1 p 2 α 2 p k α k = i = 1 k p i α i

Doc 30
0.1363
-20.0000
1.0000
0.1363
testing/wikipedia/v3/02030.html
𝚺 = λ 1 α 1 α 1 + λ 2 α 2 α 2 + + λ p α p α p

Doc 31
0.1363
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2.0000
0.2571
testing/wikipedia/v3/06805.html
C = α 1 α 2 β 1 + α 1 α 2 β 2 + α 1 β 1 β 2 + α 2 β 1 β 2
B = α 1 α 2 + α 1 β 1 + α 1 β 2 + α 2 β 1 + α 2 β 2 + β 1 β 2

Doc 32
0.1363
-28.0000
2.0000
0.1363
testing/wikipedia/v3/00282.html
det A = i 1 , i 2 , , i n = 1 n ε i 1 i n a 1 , i 1 a n , i n .

Doc 33
0.1363
-35.0000
1.0000
0.2549
testing/wikipedia/v3/28220.html
0 1 f i 1 i 2 i s ( X i 1 , X i 2 , , X i s ) d X i k = 0 ,  for  k = i 1 , , i s
0 1 f 2 ( 𝐗 ) d 𝐗 - f 0 2 = s = 1 d i 1 < < i s d f i 1 i s 2 d X i 1 d X i s

Doc 34
0.1363
-35.0000
1.0000
0.1363
testing/wikipedia/v3/03728.html
C i 1 i 2 i n ( s 1 , s 2 , , s n ) = X i 1 ( s 1 ) X i 2 ( s 2 ) X i n ( s n ) .

Doc 35
0.1363
-38.0000
1.0000
0.1363
testing/wikipedia/v3/27859.html
l = 1 n λ l x l = k = 1 n ( 1 - λ ) k - 1 λ n - k + 1 samp min ( x α 1 , x α 2 , , x α k )

Doc 36
0.1283
-7.0000
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0.1283
testing/wikipedia/v3/07729.html
α 1 β 1 α 2 β 2 α n β n

Doc 37
0.1283
-14.0000
1.0000
0.1283
testing/wikipedia/v3/03965.html
A i 1 i 2 + B i 1 i 2 = C i 1 i 2

Doc 38
0.1283
-31.0000
0.0000
0.1283
testing/wikipedia/v3/23930.html
f ( x ) = α a α x α , where  α = ( i 1 , , i r ) r , and  x α = x 1 i 1 x r i r

Doc 39
0.1283
-34.0000
0.0000
0.6530
testing/wikipedia/v3/22414.html
S ( i 1 , i 2 , , i k ) = n 1 n 2 n k 1 1 n 1 i 1 n 2 i 2 n k i k
ζ ( i 1 , i 2 , , i k ) = n 1 > n 2 > n k 1 1 n 1 i 1 n 2 i 2 n k i k
1 n i 1 σ ( 1 ) n i 2 σ ( 2 ) n i k σ ( k )
σ n 1 > n 2 > > n k 1 1 n i 1 σ ( 1 ) n i 2 σ ( 2 ) n i k σ ( k )
σ n 1 n 2 n k 1 1 n i 1 σ ( 1 ) n i 2 σ ( 2 ) n i k σ ( k )
S ( i 1 , i 2 ) = ζ ( i 1 , i 2 ) + ζ ( i 1 + i 2 )
Doc 40
0.1283
-35.0000
0.0000
0.1283
testing/wikipedia/v3/24726.html
P ( x 1 , , x l ) = i 1 + + i l d c i 1 , , i l x 1 i 1 x 2 i 2 x l i l

Doc 41
0.1283
-51.0000
1.0000
0.1283
testing/wikipedia/v3/03797.html
( i ) f ( ( i ) ρ ) = α 1 , α 2 , , α i = 1 n i r α 1 r α 2 r α i f ρ α 1 α 2 α i .

Doc 42
0.1208
-15.0000
0.0000
0.1208
testing/wikipedia/v3/25216.html
Π i 2 j 2 i 2 Π i 1 j 1 i 1 f j 1 j 2 g

Doc 43
0.1187
-16.0000
0.0000
0.1187
testing/wikipedia/v3/22392.html
H = i 1 i 2 i n G i 1 , i 2 i n

Doc 44
0.1187
-26.0000
1.0000
0.2374
testing/wikipedia/v3/23903.html
P = i 1 = S 1 , i 2 = S 2 , . . i n = S n K i 1 i 2 . . i n
P = i n = S n , . . i 2 = S 2 , i 1 = S 1 K i 1 i 2 . . i n

Doc 45
0.1187
-26.0000
0.0000
0.1187
testing/wikipedia/v3/10020.html
i = 1 2 ( 1 2 ω 2 Y i 2 M i ) = i = 1 2 ( 1 2 K i Y i 2 )

Doc 46
0.1187
-34.0000
0.0000
0.1187
testing/wikipedia/v3/16280.html
CR ( x 1 , , x N ) = i 1 , , i N = - 1 2 f i 1 i N j = 1 N b i j ( x j )

Doc 47
0.1126
-38.0000
2.0000
0.1126
testing/wikipedia/v3/05725.html
{ i 1 - i 2 - i 3 = 0 - R 2 i 2 + ϵ 1 - R 1 i 1 = 0 - R 3 i 3 - ϵ 2 - ϵ 1 + R 2 i 2 = 0

Doc 48
0.1126
-44.0000
1.0000
0.1126
testing/wikipedia/v3/24841.html
f ( 𝐱 ) = i 1 = 1 I 1 i 2 = 1 I 2 i N = 1 I N n = 1 N w n , i n ( x n ) s i 1 , i 2 , , i N ,

Doc 49
0.1071
-34.0000
1.0000
0.1071
testing/wikipedia/v3/03496.html
| M | = l = 1 n ( - 2 ) l - 1 i 1 i 2 i l | M i 1 M i 2 M i l |

Doc 50
0.0916
-37.0000
2.0000
0.0916
testing/wikipedia/v3/20862.html
W ( λ 1 , λ 2 ) = p = 1 N μ p α p ( λ 1 α p + λ 2 α p + λ 1 - α p λ 2 - α p - 3 )

Doc 51
0.0766
-32.0000
1.0000
0.0766
testing/wikipedia/v3/26341.html
V m n = 1 n m i 1 = 1 n i m = 1 n h ( x i 1 , x i 2 , , x i m ) ,

Doc 52
0.0714
-41.0000
0.0000
0.0714
testing/wikipedia/v3/29374.html
1 = a 1 1 i 1 + a 2 i 1 i 2 + a 3 i 2 i 3 + + a n i n - 1 i n + 1 i n

Doc 53
0.0471
-18.0000
1.0000
0.0471
testing/wikipedia/v3/02771.html
D α = 1 i | α | x 1 α 1 x 2 α 2 x n α n .

Doc 54
0.0430
-31.0000
0.0000
0.0430
testing/wikipedia/v3/11185.html
( x i 1 , σ j 1 ) ( x i 2 , σ j 2 ) = ( x i 1 + i 2 2 j 1 , σ j 1 + j 2 )

Doc 55
0.0403
-19.0000
2.0000
0.0403
testing/wikipedia/v3/05651.html
i 2 = [ ( 1 + i 1 n 1 ) n 1 n 2 - 1 ] × n 2

Doc 56
0.0403
-30.0000
1.0000
0.0403
testing/wikipedia/v3/14792.html
( i 1 × i 2 ) * ( γ H 1 × H 2 ) = ( i 1 ) * ( γ H 1 ) ( i 2 ) * ( γ H 2 ) ,

Doc 57
0.0357
-15.0000
2.0000
0.0357
testing/wikipedia/v3/01133.html
[ 1 ] [ 1 2 2 1 ] [ 1 2 3 2 3 1 3 1 2 ]