Returned 100 matches (100 formulae, 53 docs)
    Lookup 5.870 ms, Re-ranking 1172.502 ms
    Found 88932 tuple postings, 44940 formulae, 10804 documents
[ formulas ] [ documents ] [ documents-by-formula ]

1.0000
1 + 1 2 + 1 5 + 1 5 + 1 4 +

0.6912
1 + 1 2 + 1 2 + 1 2 + 1 2 +

0.6269
1 + 1 1 + 1 1 + 1 5 + 1 1 + 1 4 +

0.5931
2 = 1 + 1 2 + 1 2 + 1 2 + 1 2 + .

0.5882
1 + 1 1 + 1 1 + 1 1 + 1 1 +

0.5612
1 + 1 1 + 1 2 + 1 1 + 1 2 + 1 1 +

0.5588
2 + 1 4 + 1 4 + 1 4 + 1 4 +

0.5550
e = 2 + 1 1 + 1 2 + 1 1 + 1 1 + 1 4 +

0.5145
x = 1 + 1 1 + 1 1 + 1 1 + 1 1 +

0.4980
1 + 1 4 + 1 1 + 1 18 + 1

0.4955
1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 +

0.4898
2 + 1 2 + 1 2 + 1 2 + 1

0.4521
1 3 + 1 1 + 1 1 + 1 3 + 1 9 +

0.4278
2 = 1 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + .

0.4079
x = 1 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + = 2 .

0.4031
δ S = 2 + 1 2 + 1 2 + 1 2 + .

0.3675
π = 4 1 + 1 2 3 + 2 2 5 + 3 2 7 + 4 2 9 +

0.3675
π = 4 1 + 1 2 2 + 3 2 2 + 5 2 2 + 7 2 2 +

0.3646
π = 4 1 + 1 2 2 + 3 2 2 + 5 2 2 + 7 2 2 + .

0.3601
x = 1 + z 1 + z 1 + z 1 + z 1 +

0.3590
a 0 + 1 a 1 + 1 a 2 + 1 + 1 a n ,

0.3518
1 1 + 1 0 + 1 8 + 1 4 + 1 1 + 1 0 + 1 /

0.3492
φ = 1 + 1 1 + 1 1 + 1 1 +

0.3446
11 = 3 + 1 3 + 1 6 + 1 3 + 1 6 + 1 3 +

0.3245
π = 4 1 + 1 2 3 + 2 2 5 + 3 2 7 +

0.3205
577 408 = 1 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 .

0.3161
x = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + 1

0.3109
π = 2 + 4 3 + 1 3 4 + 3 5 4 + 5 7 4 +

0.3060
tanh 1 2 = e - 1 e + 1 = 0 + 1 2 + 1 6 + 1 10 + 1 14 + 1

0.3039
e z = 1 + z 1 + - z 2 + z 3 + - 2 z 4 + 2 z 5 +

0.2997
23 16 = 1 + 1 2 + 1 3 + 1 2 = [ 1 ; 2 , 3 , 2 ] ,

0.2898
S = a 0 + 1 a 1 + 1 a 2 + 1 a 3 +

0.2857
π = 3 + 1 7 + 1 15 + 1 1 + 1 292 + 1 1 + 1 1 + 1 1 +

0.2857
x = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + .

0.2833
c 0 + K n = 1 1 c n = c 0 + 1 c 1 + 1 c 2 + 1 c 3 + 1 c 4 +

0.2833
n + 1 n + 1 n + 1 n + 1 n + = [ n ; n , n , n , n , ] = 1 2 ( n + n 2 + 4 )

0.2800
a + 1 b + 1 c + 1

0.2757
e z = 1 1 + - z 1 + z 2 + - z 3 + 2 z 4 + - 2 z 5 +

0.2720
π = 3 + 1 2 6 + 3 2 6 + 5 2 6 + 7 2 6 +

0.2659
φ = [ 1 ; 1 , 1 , 1 , ] = 1 + 1 1 + 1 1 + 1 1 +

0.2658
4 π = 1 + 1 2 2 + 3 2 2 + 5 2 2 + 7 2 2 + 9 2 2 +

0.2642
a 1 + 1 a 2 + 1 a 3 + 1

0.2597
arctan z = z 1 + ( 1 z ) 2 3 + ( 2 z ) 2 5 + ( 3 z ) 2 7 + ( 4 z ) 2 9 + ,

0.2586
I 1 ( 2 ) I 0 ( 2 ) = n = 0 n n ! n ! n = 0 1 n ! n ! = 1 1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + 1 /

0.2541
tan ( x ) = x 1 + - x 2 3 + - x 2 5 + - x 2 7 +

0.2523
a 0 + 1 a 1 + 1 a 2 + 1 a 3

0.2517
x = 1 1 + a 2 1 + a 3 1 + a 4 1 +

0.2478
e = 1 + 2 1 + 1 6 + 1 10 + 1 14 + 1 18 + 1 22 + 1 26 + .

0.2474
π 4 = 1 1 + 1 2 2 + 3 2 2 + 5 2 2 + 7 2 2 + 9 2 2 +

0.2455
φ - 1 = [ 0 ; 1 , 1 , 1 , ] = 0 + 1 1 + 1 1 + 1 1 +

0.2410
f ( z ) = 1 + z 1 + z 1 + z 1 + z .

0.2389
( 1 - z ) - b = 1 1 + - b z 1 + ( b - 1 ) z 2 + - ( b + 1 ) z 3 + 2 ( b - 2 ) z 4 +

0.2387
x = 1 + x - 1 2 + x - 1 2 + x - 1 2 +

0.2369
r = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + ,

0.2312
x = b 0 + a 1 b 1 + a 2 b 2 + a 3 b 3 + a 4 b 4 +

0.2302
y = 1 + z 1 + z 1 + z 1 +

0.2289
x = 1 1 + a 2 b 2 + a 3 b 3 + a 4 b 4 +

0.2284
x = [ a 0 ; a 1 , a 2 , a 3 , ] = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + 1 ,

0.2283
x = b 0 + a 1 b 1 + a 2 b 2 + a 3 b 3 + a 4 b 4 + .

0.2270
L ( x ) = x 3 + x 2 5 + x 2 7 + x 2 9 +

0.2260
1 15 + 1 1 + 1 102

0.2249
f 1 f 0 = 1 1 + k 1 z 1 + k 2 z 1 + k 3 z 1 +

0.2236
p ( z ) = a 0 z + a 1 z + a 2 z + a 3 z +

0.2222
π = 3 + 1 2 6 + 3 2 6 + 5 2 6 +

0.2213
e = 2 + 1 1 + 2 5 + 1 10 + 1 14 + 1 18 + = 1 + 2 1 + 1 6 + 1 10 + 1 14 + 1 18 +

0.2197
a 0 + b 1 a 1 + b 2 a 2 + b 3 a 3 +

0.2191
x = K 1 1 z = 1 z + 1 z + 1 z +

0.2184
q = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + 1 + 1 a k = [ a 0 ; a 1 , a 2 , , a k ]

0.2179
x = a 0 + 1 a 1 + 1 a 2 + 1 a 3

0.2178
x = [ a 0 ; a 1 , a 2 , ] = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + 1 a 4 + = a 0 + K i = 1 1 a i ,

0.2173
a b = q 0 + 1 q 1 + 1 q 2 + 1 + 1 q N = [ q 0 ; q 1 , q 2 , , q N ] .

0.2126
e 2 = 1 + 4 0 + 2 2 6 + 2 2 10 + 2 2 14 + = 7 + 2 5 + 1 7 + 1 9 + 1 11 +

0.2126
Γ ( s , z ) = z s e - z z + 1 - s 1 + 1 z + 2 - s 1 + 2 z + 3 - s 1 +

0.2117
f ( z ) = 1 1 + c 2 z 1 + c 3 z 1 + c 4 z 1 +

0.2045
- 3 + 1 2 + 1 18

0.2028
1 + q 1 + q 2 1 + q 3 1 + = G ( q ) H ( q ) .

0.1964
a 1 b 1 + a 2 b 2 + a 3 b 3 +

0.1936
e = 2 + 1 1 + 1 2 + 2 3 + 3 4 + 4 5 + = 2 + 2 2 + 3 3 + 4 4 + 5 5 + 6 6 +

0.1839
π 4 = 1 1 + 1 2 2 + 3 2 2 + 5 2 2 + = 1 - 1 3 + 1 5 - 1 7 + -

0.1778
2 c + 2 d + 2 4 = a

0.1774
π = 3 + 1 7 + 1 15 + 1 1 + 1 292 + 1 1 + 1 1 + 1 1 + 1 2 + 1 1 + 1 3 + 1 1 +

0.1772
F 1 0 ( a + 1 ; z ) a 0 F 1 ( a ; z ) = 1 a + z ( a + 1 ) + z ( a + 2 ) + z ( a + 3 ) +

0.1722
G = 1 1 + 1 1 + 1 1 + 2 1 + 2 1 + 3 1 + 3 1 + 4 1 1 + .

0.1718
[ 1 ; 2 , 3 , 1 ] = [ 1 ; 2 , 4 ] = 1 + 1 2 + 1 4 = 13 9 .

0.1712
[ 2 ; - 4 , - 4 , - 4 , ] = 2 - 1 4 - 1 4 - 1 4 -

0.1680
x = 1 + 1 1 + ( 1 + 1 1 + x ) = 1 + 1 2 + 1 1 + x .

0.1654
x = z - 1 1 + z - 2 1 + z - 2 1 +

0.1561
log 2 = log ( 1 + 1 ) = 1 1 + 1 2 + 1 3 + 2 2 + 2 5 + 3 2 + = 2 3 - 1 2 9 - 2 2 15 - 3 2 21 -

0.1513
ln 2 = 1 1 + 1 2 + 1 3 + 2 2 + 2 5 + 3 2 + 3 7 + 4 2 + = 2 3 - 1 2 9 - 2 2 15 - 3 2 21 -

0.1472
e 3 = 1 + 6 - 1 + 3 2 6 + 3 2 10 + 3 2 14 + = 13 + 54 7 + 9 14 + 9 18 + 9 22 +

0.1446
e z = 1 + 2 z 2 - z + z 2 6 + z 2 10 + z 2 14 +

0.1434
1 1 + e - 2 π 1 + e - 4 π 1 + e - 6 π 1 + = ( 5 + 5 2 - 5 + 1 2 ) e 2 π / 5 = e 2 π / 5 ( φ 5 - φ ) .

0.1420
4 0 x e - x 5 cosh x d x = 1 1 + 1 2 1 + 1 2 1 + 2 2 1 + 2 2 1 + 3 2 1 + 3 2 1 + .

0.1404
π = 4 1 + 1 2 3 + 2 2 5 + 3 2 7 + = 4 - 1 + 1 6 - 1 34 + 16 3145 - 4 4551 + 1 6601 - 1 38341 + -

0.1392
1 1 + 1 2 2 + 3 2 2 = 13 15 = 1 - 1 3 + 1 5 .

0.1303
π = 4 1 + 1 2 2 + 3 2 2 + 5 2 2 + = n = 0 4 ( - 1 ) n 2 n + 1 = 4 1 - 4 3 + 4 5 - 4 7 + -

0.1294
f ( z ) = a 1 z 1 + a 2 z 1 + a 3 z 1 + a 4 z

0.1271
π = 2 + 2 1 + 1 1 / 2 + 1 1 / 3 + 1 1 / 4 + = 2 + 2 1 + 1 2 1 + 2 3 1 + 3 4 1 +

0.1043
π = 4 n = 0 ( - 1 ) n 2 n + 1 = 4 ( 1 1 - 1 3 + 1 5 - 1 7 + - ) = 4 1 + 1 2 2 + 3 2 2 + 5 2 2 +

0.0833
1 + 1 2 + 1 3 + 1 4 + 1 5 +