Returned 100 matches (100 formulae, 53 docs)
    Lookup 5.870 ms, Re-ranking 1437.384 ms
    Found 88932 tuple postings, 44940 formulae, 10804 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
1.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Backhouse's_constant.html
1 + 1 2 + 1 5 + 1 5 + 1 4 +

Doc 2
0.8456
1.5711
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Square_root_of_2.html
1 + 1 2 + 1 2 + 1 2 + 1 2 +
2 = 1 + 1 2 + 1 2 + 1 2 + 1 2 + .

Doc 3
0.7941
1.5520
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Golden_ratio.html
1 + 1 1 + 1 1 + 1 1 + 1 1 +
φ = [ 1 ; 1 , 1 , 1 , ] = 1 + 1 1 + 1 1 + 1 1 +
φ - 1 = [ 0 ; 1 , 1 , 1 , ] = 0 + 1 1 + 1 1 + 1 1 +
Doc 4
0.7794
1.2454
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Square_root_of_5.html
2 + 1 4 + 1 4 + 1 4 + 1 4 +
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 + .
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 ) .
Doc 5
0.7194
0.7194
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Lieb's_square_ice_constant.html
1 + 1 1 + 1 1 + 1 5 + 1 1 + 1 4 +

Doc 6
0.6945
2.4693
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Generalized_continued_fraction.html
x = 1 + 1 1 + 1 1 + 1 1 + 1 1 +
x = 1 + z 1 + z 1 + z 1 + z 1 +
tan ( x ) = x 1 + - x 2 3 + - x 2 5 + - x 2 7 +
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 -
x = b 0 + a 1 b 1 + a 2 b 2 + a 3 b 3 + a 4 b 4 +
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 + -
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 + -

Doc 7
0.6918
0.6918
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Bernstein's_constant.html
1 3 + 1 1 + 1 1 + 1 3 + 1 9 +

Doc 8
0.6866
0.9126
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Square_root_of_3.html
1 + 1 1 + 1 2 + 1 1 + 1 2 + 1 1 +
[ 2 ; - 4 , - 4 , - 4 , ] = 2 - 1 4 - 1 4 - 1 4 -

Doc 9
0.6449
0.6449
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Apéry's_constant.html
1 + 1 4 + 1 1 + 1 18 + 1

Doc 10
0.6408
1.1718
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Silver_ratio.html
2 + 1 2 + 1 2 + 1 2 + 1
δ S = 2 + 1 2 + 1 2 + 1 2 + .

Doc 11
0.6358
0.6358
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Transcendental_number.html
1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 +

Doc 12
0.6335
2.9372
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Gauss's_continued_fraction.html
e = 2 + 1 1 + 1 2 + 1 1 + 1 1 + 1 4 +
e z = 1 + z 1 + - z 2 + z 3 + - 2 z 4 + 2 z 5 +
e z = 1 1 + - z 1 + z 2 + - z 3 + 2 z 4 + - 2 z 5 +
f 1 f 0 = 1 1 + k 1 z 1 + k 2 z 1 + k 3 z 1 +
arctan z = z 1 + ( 1 z ) 2 3 + ( 2 z ) 2 5 + ( 3 z ) 2 7 + ( 4 z ) 2 9 + ,
( 1 - z ) - b = 1 1 + - b z 1 + ( b - 1 ) z 2 + - ( b + 1 ) z 3 + 2 ( b - 2 ) z 4 +
π 4 = 1 1 + 1 2 2 + 3 2 2 + 5 2 2 + = 1 - 1 3 + 1 5 - 1 7 + -
F 1 0 ( a + 1 ; z ) a 0 F 1 ( a ; z ) = 1 a + z ( a + 1 ) + z ( a + 2 ) + z ( a + 3 ) +

Doc 13
0.5541
0.9499
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Pell_number.html
2 = 1 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + .
577 408 = 1 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 .

Doc 14
0.5407
1.6026
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
π = 4 1 + 1 2 3 + 2 2 5 + 3 2 7 + 4 2 9 +
π = 4 1 + 1 2 2 + 3 2 2 + 5 2 2 + 7 2 2 +
π = 3 + 1 2 6 + 3 2 6 + 5 2 6 + 7 2 6 +
Doc 15
0.5365
0.7925
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Euler's_continued_fraction_formula.html
π = 4 1 + 1 2 2 + 3 2 2 + 5 2 2 + 7 2 2 + .
x = 1 1 + a 2 b 2 + a 3 b 3 + a 4 b 4 +

Doc 16
0.5283
0.7152
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Solving_quadratic_equations_with_continued_fractions.html
x = 1 + 1 2 + 1 2 + 1 2 + 1 2 + 1 2 + = 2 .
x = 1 + 1 1 + ( 1 + 1 1 + x ) = 1 + 1 2 + 1 1 + x .

Doc 17
0.5274
0.5274
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Square_root.html
11 = 3 + 1 3 + 1 6 + 1 3 + 1 6 + 1 3 +

Doc 18
0.5078
2.8148
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Continued_fraction.html
π = 2 + 4 3 + 1 3 4 + 3 5 4 + 5 7 4 +
1 15 + 1 1 + 1 102
x = 1 + x - 1 2 + x - 1 2 + x - 1 2 +
- 3 + 1 2 + 1 18
a 0 + 1 a 1 + 1 a 2 + 1 a 3
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 +
x = b 0 + a 1 b 1 + a 2 b 2 + a 3 b 3 + a 4 b 4 +
a 0 + b 1 a 1 + b 2 a 2 + b 3 a 3 +
x = a 0 + 1 a 1 + 1 a 2 + 1 a 3
π = 3 + 1 7 + 1 15 + 1 1 + 1 292 + 1 1 + 1 1 + 1 1 + 1 2 + 1 1 + 1 3 + 1 1 +

Doc 19
0.5000
0.5000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Fibonacci_number.html
φ = 1 + 1 1 + 1 1 + 1 1 +

Doc 20
0.4967
1.0963
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Approximations_of_π.html
π = 4 1 + 1 2 3 + 2 2 5 + 3 2 7 +
π = 3 + 1 2 6 + 3 2 6 + 5 2 6 +
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 +
Doc 21
0.4824
0.8017
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
1 1 + 1 0 + 1 8 + 1 4 + 1 1 + 1 0 + 1 /
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 /

Doc 22
0.4324
1.0401
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/William_Brouncker,_2nd_Viscount_Brouncker.html
4 π = 1 + 1 2 2 + 3 2 2 + 5 2 2 + 7 2 2 + 9 2 2 +
π 4 = 1 1 + 1 2 2 + 3 2 2 + 5 2 2 + 7 2 2 + 9 2 2 +
1 1 + 1 2 2 + 3 2 2 = 13 15 = 1 - 1 3 + 1 5 .
Doc 23
0.4235
0.4235
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Singly_and_doubly_even.html
tanh 1 2 = e - 1 e + 1 = 0 + 1 2 + 1 6 + 1 10 + 1 14 + 1

Doc 24
0.3907
1.8034
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Convergence_problem.html
x = 1 1 + a 2 1 + a 3 1 + a 4 1 +
y = 1 + z 1 + z 1 + z 1 +
f ( z ) = 1 1 + c 2 z 1 + c 3 z 1 + c 4 z 1 +
x = z - 1 1 + z - 2 1 + z - 2 1 +
x = b 0 + a 1 b 1 + a 2 b 2 + a 3 b 3 + a 4 b 4 + .
x = K 1 1 z = 1 z + 1 z + 1 z +
Doc 25
0.3857
0.3857
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pi.html
π = 3 + 1 7 + 1 15 + 1 1 + 1 292 + 1 1 + 1 1 + 1 1 +

Doc 26
0.3590
0.3590
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Rational_number.html
a 0 + 1 a 1 + 1 a 2 + 1 + 1 a n ,

Doc 27
0.3583
0.7691
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Stern–Brocot_tree.html
23 16 = 1 + 1 2 + 1 3 + 1 2 = [ 1 ; 2 , 3 , 2 ] ,
q = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + 1 + 1 a k = [ a 0 ; a 1 , a 2 , , a k ]
[ 1 ; 2 , 3 , 1 ] = [ 1 ; 2 , 4 ] = 1 + 1 2 + 1 4 = 13 9 .
Doc 28
0.3575
0.3575
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/E_(mathematical_constant).html
e = 1 + 2 1 + 1 6 + 1 10 + 1 14 + 1 18 + 1 22 + 1 26 + .

Doc 29
0.3558
0.3558
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Brillouin_and_Langevin_functions.html
L ( x ) = x 3 + x 2 5 + x 2 7 + x 2 9 +

Doc 30
0.3388
0.3388
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Complex_plane.html
f ( z ) = 1 + z 1 + z 1 + z 1 + z .

Doc 31
0.3322
0.8354
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Exponential_function.html
e 2 = 1 + 4 0 + 2 2 6 + 2 2 10 + 2 2 14 + = 7 + 2 5 + 1 7 + 1 9 + 1 11 +
e 3 = 1 + 6 - 1 + 3 2 6 + 3 2 10 + 3 2 14 + = 13 + 54 7 + 9 14 + 9 18 + 9 22 +
e z = 1 + 2 z 2 - z + z 2 6 + z 2 10 + z 2 14 +
Doc 32
0.3161
0.3161
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Khinchin's_constant.html
x = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + 1

Doc 33
0.3161
0.3161
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Borel_set.html
x = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + 1

Doc 34
0.3112
0.3112
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Rogers–Ramanujan_identities.html
1 + q 1 + q 2 1 + q 3 1 + = G ( q ) H ( q ) .

Doc 35
0.2988
0.5837
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/List_of_representations_of_e.html
e = 2 + 1 1 + 2 5 + 1 10 + 1 14 + 1 18 + = 1 + 2 1 + 1 6 + 1 10 + 1 14 + 1 18 +
e = 2 + 1 1 + 1 2 + 2 3 + 3 4 + 4 5 + = 2 + 2 2 + 3 3 + 4 4 + 5 5 + 6 6 +

Doc 36
0.2955
0.2955
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Incomplete_gamma_function.html
Γ ( s , z ) = z s e - z z + 1 - s 1 + 1 z + 2 - s 1 + 2 z + 3 - s 1 +

Doc 37
0.2898
0.2898
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Methods_of_computing_square_roots.html
S = a 0 + 1 a 1 + 1 a 2 + 1 a 3 +

Doc 38
0.2857
0.2857
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Hermite's_problem.html
x = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + .

Doc 39
0.2833
0.2833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Infinite_expression_(mathematics).html
c 0 + K n = 1 1 c n = c 0 + 1 c 1 + 1 c 2 + 1 c 3 + 1 c 4 +

Doc 40
0.2833
0.2833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Metallic_mean.html
n + 1 n + 1 n + 1 n + 1 n + = [ n ; n , n , n , n , ] = 1 2 ( n + n 2 + 4 )

Doc 41
0.2807
0.2807
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Gompertz_constant.html
G = 1 1 + 1 1 + 1 1 + 2 1 + 2 1 + 3 1 + 3 1 + 4 1 1 + .

Doc 42
0.2800
0.2800
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Budan's_theorem.html
a + 1 b + 1 c + 1

Doc 43
0.2642
0.2642
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Vincent's_theorem.html
a 1 + 1 a 2 + 1 a 3 + 1

Doc 44
0.2613
0.2613
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Mathematical_constant.html
r = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + ,

Doc 45
0.2284
0.2284
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Complete_quotient.html
x = [ a 0 ; a 1 , a 2 , a 3 , ] = a 0 + 1 a 1 + 1 a 2 + 1 a 3 + 1 ,

Doc 46
0.2278
0.2278
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Help:Displaying_a_formula.html
2 c + 2 d + 2 4 = a

Doc 47
0.2236
0.2236
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Factorial.html
p ( z ) = a 0 z + a 1 z + a 2 z + a 3 z +

Doc 48
0.2178
0.2178
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Restricted_partial_quotients.html
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 ,

Doc 49
0.2177
0.2177
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
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 -

Doc 50
0.2173
0.2173
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Euclidean_algorithm.html
a b = q 0 + 1 q 1 + 1 q 2 + 1 + 1 q N = [ q 0 ; q 1 , q 2 , , q N ] .

Doc 51
0.2000
0.2000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Chain_sequence.html
f ( z ) = a 1 z 1 + a 2 z 1 + a 3 z 1 + a 4 z

Doc 52
0.1964
0.1964
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Śleszyński–Pringsheim_theorem.html
a 1 b 1 + a 2 b 2 + a 3 b 3 +

Doc 53
0.0833
0.0833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Logarithmic_growth.html
1 + 1 2 + 1 3 + 1 4 + 1 5 +