Returned 90 matches (100 formulae, 80 docs)
    Lookup 4.578 ms, Re-ranking 659.901 ms
    Found 68715 tuple postings, 42887 formulae, 10694 documents
[ formulas ] [ documents ] [ documents-by-formula ]

1.0000
w = { w * if  w * > 1 2 , 1 2 if  w * 1 2 .

0.3545
y i = { y i * if y i * > y L y L if y i * y L .

0.3493
y i = { y i * if y i * > 0 0 if y i * 0

0.3208
y 1 i = { y 1 i * if y 1 i * > 0 0 if y 1 i * 0.
y 2 i = { y 2 i * if y 1 i * > 0 0 if y 1 i * 0.
y 3 i = { y 3 i * if y 1 i * > 0 0 if y 1 i * 0.
0.3011
Π ( t ) = def { 1 if | t | < 1 2 , 0 if | t | > 1 2 .

0.2758
y i = { y i * if y i * < y U y U if y i * y U .

0.2527
Y = { 0 , if Y * > 0 1 , if Y * < 0.

0.2362
Y 1 = { 1 if Y 1 * > 0 , 0 otherwise ,
Y 2 = { 1 if Y 2 * > 0 , 0 otherwise ,

0.2255
𝐚 i = { 1 if w i > 0 , 0 if w i < 0.

0.2199
w = { w m i n , if w m i n w ( L ) w ( L ) , if w m i n w ( L )

0.2160
Y n = { 1 , if U n > 0 , 0 , if U n 0

0.2160
f ( x ) = { 1 x if x > 0 , 5 if x 0.

0.2158
rect ( t ) = Π ( t ) = { 0 if | t | > 1 2 1 2 if | t | = 1 2 1 if | t | < 1 2 .

0.2109
{ x * log ( x * ) - x * if x * > 0 0 if x * = 0

0.2009
x + α = { x α if x > 0 0 otherwise

0.1900
g = { - 5 9 ( x 2 + 1 ) S , if T > 1 2 5 9 ( x 2 + 1 ) S , if T < 1 2 0 , if T = 0

0.1896
f ( x ) = { exp ( - 1 / x ) if x > 0 , 0 if x 0 ,

0.1882
δ b a = { 1 if a = b , 0 if a b .

0.1875
δ i j = { 0 if i j , 1 if i = j .

0.1852
| a | = { a , if a 0 - a , if a 0

0.1839
ω = { D if D 2 , 3 ( mod 4 ) 1 + D 2 if D 1 ( mod 4 )

0.1781
( n k ) = { n k ¯ / k ! if k n 2 n n - k ¯ / ( n - k ) ! if k > n 2 .

0.1773
Y i = { 1 if Y i 1 > Y i 0 , 0 otherwise.

0.1771
𝟏 A ( x ) = { 1 if x A , 0 if x A .
χ A ( x ) = { 1 if x A , 0 if x A .

0.1745
f ( x ) = { x if x 0 , 0 if x < 0

0.1722
f ( n ) ( x ) = { p n ( x ) x 2 n f ( x ) if x > 0 , 0 if x 0 ,

0.1676
M ( n ) = { n - 10 , if n > 100 M ( M ( n + 11 ) ) , if n 100

0.1619
a z = { z if a > 0 , - z if a < 0.

0.1616
{ x * log ( x * ) - ( 1 + x * ) log ( 1 + x * ) if x * > 0 0 if x * = 0

0.1611
V o = { 1 , if V + > V - 0 , if V + < V -

0.1604
I | X | K = { 1 if | X | K , 0 if | X | < K .

0.1570
f ( t ) = { t 1 / 3 if t > ( 6 29 ) 3 1 3 ( 29 6 ) 2 t + 4 29 otherwise

0.1567
( x 2 p ) = { 1 if p x 0 if p x .

0.1500
f ( x ) = { x 2 sin ( 1 x ) if x 0 , 0 if x = 0

0.1484
δ ( a , b ) = { 1 if a = b 0 if a < b .

0.1478
χ i , χ j = { 0 if i j , 1 if i = j .

0.1476
( a - 1 ) = { - 1 if a < 0 , 1 if a 0.

0.1423
ρ ( x , y ) = { 1 if x y , 0 if x = y

0.1405
{ x } + { - x } = { 0 if x 1 if x .

0.1394
ϕ ( x ) = { 1 if x > x 0 0 if x < x 0
ϕ ( T ) = { 1 if T > t 0 0 if T < t 0

0.1389
𝟏 A ( ω ) = { 1 if ω A , 0 if ω A ,

0.1385
f p SS ( x ) = { - log x if p = 0 1 - x p p otherwise.

0.1368
rect ( t ) = Π ( t ) = lim n , n ( Z ) 1 ( 2 t ) 2 n + 1 = { 0 if | t | > 1 2 1 2 if | t | = 1 2 1 if | t | < 1 2 .

0.1350
f ( x ) = { + x 2 , if x 0 - x 2 , if x 0.

0.1339
δ 0 = { 1 if X 1 = 0 , 0 otherwise,

0.1338
f ( k ; p ) = { p if k = 1 , 1 - p if k = 0.

0.1338
f ( x ) = { + 2 x , if x 0 - 2 x , if x 0.

0.1320
= { 1 T ( 1 + t T ) if 0 t < T 1 T ( 1 - t T ) if T t < 2 T 0 otherwise

0.1319
f ( x ) = { 1 if x > 0 0 otherwise

0.1319
y n i = { 1 , if U n i > U n j , j i , 0 , otherwise

0.1313
I ( y j ) = { 0 if y j = y L 1 if y j y L .

0.1310
{ n if k = 0 n + 1 k + 1 if 1 k n .

0.1292
𝐈 O := { 1 if x > median , 0 otherwise .
𝐈 O := { 1 if x > μ , 0 otherwise .

0.1285
𝟏 A ( x ) := { 1 if x A , 0 if x A .
𝟏 S ( x ) := { 1 if x S , 0 if x S .

0.1284
f ( x ) = { 1 , if | x | < 1 2 , 0 , otherwise .

0.1278
B 2 k = { c 0 , if k = 0 , c k / k , if k > 0 ,

0.1266
u i T u j = { 1 , if i = j , 0 , if i j E .

0.1265
e m , e n = { 1 if m = n 0 if m n .

0.1263
d ( x , y ) := { 0 if x = y , 1 if x y .

0.1262
f ( x ) = { sin ( 1 / x ) if x 0 , 1 if x = 0 ,

0.1262
f ( P , w ) = { 0 if w 1 in G undefined/does not halt if w = 1 in G

0.1250
θ = { sin - 1 1 β , if β 1 π - sin - 1 β , if β 1

0.1231
f ( w ) = { 0 if w 1 in H undefined/does not halt if w = 1 in H .
h ( w ) = { 0 if w 1 in S undefined/does not halt if w = 1 in S .

0.1228
θ ^ n H = { θ ^ n , if | θ ^ n | n - 1 / 4 , and 0 , if | θ ^ n | < n - 1 / 4 .

0.1223
n ! = { 1 if n = 0 , ( n - 1 ) ! × n if n > 0

0.1208
f ( P , w ) = { 0 if w 1 in H undefined/does not halt if w = 1 in H .

0.1205
y i ( λ ) = { y i λ - 1 λ if λ 0 , ln ( y i ) if λ = 0 ,

0.1205
Ω = { tan π α 2 if α 1 , - 2 π log | t | if α = 1.

0.1174
P = { - 1 + p 2 , if p = 4 m + 1 , - 1 + i p 2 , if p = 4 m + 3.

0.1173
V i + k , j = { 0 , if j k ; ( j - 1 ) ! ( j - k - 1 ) ! α i j - k - 1 , if j > k .

0.1155
μ ( A ) = { 1 if 0 A 0 if 0 A .

0.1140
P i j ( ν ) = { 1 4 + 3 4 e - 4 ν / 3 if i = j 1 4 - 1 4 e - 4 ν / 3 if i j

0.1123
T = { 1 2 π arctan r g + 1 4 , if g > 0 1 2 π arctan r g + 3 4 , if g < 0 0 , if g = 0

0.1111
m ( f , z 0 ) = λ = { f c ( z 0 ) , if z 0 1 f c ( z 0 ) , if z 0 =

0.1095
0 π cos m x cos n x d x = { 0 if m n π 2 if m = n m , n positive integers
0 π sin m x sin n x d x = { 0 if m n π 2 if m = n m , n positive integers

0.1080
P j ( d j ) = { 0 if d j 0 1 if d j > 0

0.1078
φ ( θ ) = { 1 + 2 θ π , if θ [ - π , 0 ] , 1 - 2 θ π , if θ [ 0 , π ] .

0.1073
H ( t ) = { 0 , if t 0 ; 1 , if t > 0.

0.1046
D R * ( n ) = { D R ( n ) 2 , if D R ( n ) is even D R ( n ) + 9 2 , if D R ( n ) is odd

0.1028
C ( μ ) = { 1 , if f ( a ) < μ < f ( b ) ; 1 2 , if μ = f ( a ) or μ = f ( b ) ;

0.1016
μ ( A ) = { ( 1 - 1 λ ) 𝟏 0 A + ν ( A ) , if λ > 1 ν ( A ) , if 0 λ 1 ,

0.0993
Y = { X if | X | c - X if | X | > c

0.0954
E [ T k ] = { ( ν 2 ) k 2 Γ ( ν - k 2 ) Γ ( ν 2 ) exp ( - μ 2 2 ) d k d μ k exp ( μ 2 2 ) , if ν > k ; Does not exist , if ν k .

0.0948
( y ) = { 1 2 - t y if t y 0 , 1 2 ( 1 - t y ) 2 if 0 < t y 1 , 0 if 1 t y

0.0882
| x | = { x if 1 x p - 1 2 , p - x if p + 1 2 x p - 1.

0.0777
F ( x ) = { 1 if x λ 0 if x > λ
K ( x ) = { 1 if x λ 0 if x > λ

0.0699
G ( s y m b o l x - s y m b o l r ) = { 1 Δ , if | s y m b o l x - s y m b o l r | Δ 2 , 0 , otherwise .

0.0623
c F ( a , b ) = { 1 2 | b | , if | a | < | b | 0 , if | a | > | b |

0.0387
absolute margin of victory = { 0 ; w c 2 w - max { r , c 2 } ; w > c 2

0.0353
normalized margin of victory = { 0 ; w c 2 w - max { r , c 2 } c 2 ; w > c 2