Returned 95 matches (100 formulae, 55 docs)
    Lookup 16.844 ms, Re-ranking 0.169 ms
    Found 222920 tuple postings, 88494 formulae, 15993 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
1.0000
2.5377
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
x - 1 - 1 2 - 1 4 - 1 5 - 1 6 - 1 9 - = 1
x - 1 = 1 + 1 2 + 1 4 + 1 5 + 1 6 + 1 9 +
x - 1 - 1 2 = 1 + 1 5 + 1 6 + 1 7 + 1 10 + 1 11 + 1 12 +
x - 1 = 1 + 1 3 + 1 5 + 1 6 + 1 7 + 1 9 + 1 10 + 1 11 +
x = 1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + 1 7 + 1 8
1 2 = 1 3 + 1 9 + 1 27 + 1 81 +
1 = 1 2 + 1 4 + 1 8 + 1 16 +

Doc 2
0.4919
1.4412
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Riemann_series_theorem.html
1 - 1 2 - 1 4 + 1 3 - 1 6 - 1 8 + 1 5 - 1 10 - 1 12 +
1 - 1 2 + 1 3 - 1 4 +
1 2 - 1 4 + 1 6 - 1 8 + 1 10 + + 1 2 ( 2 k - 1 ) - 1 2 ( 2 k ) +
1 + 1 3 + + 1 2 a - 1 - 1 2 - 1 4 - - 1 2 b + 1 2 a + 1 + + 1 4 a - 1 - 1 2 b + 2 -
1 2 k - 1 - 1 2 ( 2 k - 1 ) - 1 4 k , k = 1 , 2 , .

Doc 3
0.4399
0.7071
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1::2_−_1::4_+_1::8_−_1::16_+_⋯.html
1 - 1 2 - 1 4 + 1 8 - 1 16 + = 1 3 .
1 2 - 1 4 + 1 8 - 1 16 + = 1 / 2 1 - ( - 1 / 2 ) = 1 3 .

Doc 4
0.4110
1.6566
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_series_(mathematics).html
1 - 1 2 + 1 3 - 1 4 + 1 5 - = ln 2.
n = 1 ( - 1 ) n + 1 n = 1 - 1 2 + 1 3 - 1 4 + 1 5 -
n = 0 ( - 1 ) n 2 n + 1 = 1 - 1 3 + 1 5 - 1 7 + = π 4 .
n = 1 1 n = 1 + 1 2 + 1 3 + 1 4 + 1 5 + .
1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + 1 7 + 1 8 + 1 9 +
area of rectangles = 1 + 1 2 + 1 3 + 1 4 + 1 5 + .
Doc 5
0.4092
0.4092
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Special_values_of_L-functions.html
1 - 1 3 + 1 5 - 1 7 + 1 9 - = π 4 ,

Doc 6
0.4092
0.4092
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Leibniz_formula_for_π.html
1 - 1 3 + 1 5 - 1 7 + 1 9 - = π 4 .

Doc 7
0.3797
3.4063
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
n = 1 1 n ( 2 n n ) = 1 - 1 2 + 1 4 - 1 5 + 1 7 - 1 8 +
3 3 4 ( 1 - 1 2 2 + 1 4 2 - 1 5 2 + 1 7 2 - 1 8 2 + 1 10 2 ± )
n = 1 ( - 1 ) n + 1 n ! = 1 1 ! - 1 2 ! + 1 3 ! - 1 4 ! + 1 5 ! - 1 6 ! +
n = 1 ( - 1 ) n - 1 2 2 n + 1 = 1 1 + 1 3 - 1 5 - 1 7 + 1 9 + 1 11 -
π 4 = n = 0 ( - 1 ) n 2 n + 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 -
n = 0 ( - 1 ) n n ! = 1 0 ! - 1 1 ! + 1 2 ! - 1 3 ! + 1 4 ! - 1 5 ! +
k = 1 ( - 1 ) k s k - 1 = 1 1 - 1 2 + 1 6 - 1 42 + 1 1806 ±
π 2 12 = n = 1 ( - 1 ) n + 1 n 2 = 1 1 2 - 1 2 2 + 1 3 2 - 1 4 2 + 1 5 2 -
n = 1 1 n 2 n = n = 1 ( - 1 ) n + 1 n = 1 1 - 1 2 + 1 3 - 1 4 +
π 3 32 = n = 1 - 1 n + 1 ( - 1 + 2 n ) 3 = 1 1 3 - 1 3 3 + 1 5 3 - 1 7 3 +
n = 0 ( - 1 ) n x 2 n + 1 2 n + 1 = 1 2 - 1 3 2 3 + 1 5 2 5 - 1 7 2 7 + For x = 1 / 2
= 1 π ( 1 2 - 1 3 2 3 + 1 5 2 5 - 1 7 2 7 + )
n = 1 1 n 3 = 1 1 3 + 1 2 3 + 1 3 3 + 1 4 3 + 1 5 3 + =

Doc 8
0.3675
1.0160
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
n = 1 ( - 1 ) n + 1 n = 1 - 1 2 + 1 3 - 1 4 + 1 5 -
1 - 1 2 + 1 3 - 1 4 + 1 5 - = n = 1 ( - 1 ) n + 1 1 n = ln ( 2 ) .
1 + 1 2 + 1 4 + 1 8 + + 1 2 n + .
1 + 1 2 + 1 3 + 1 4 + 1 5 + = n = 1 1 n .

Doc 9
0.3527
1.8027
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
1 1 - 1 2 + 1 4 - 1 8 + 1 16 - 1 32 + = 2 3 .
1 1 - 1 2 + 1 3 - 1 4 + 1 5 = ln ( 2 )
1 1 + 1 1 + 1 2 + 1 6 + 1 24 + 1 120 + = e .
1 1 + 1 3 + 1 6 + 1 10 + 1 15 + 1 21 + = 2.
1 1 + 1 2 + 1 4 + 1 8 + 1 16 + 1 32 + = 2.
1 1 + 1 1 + 1 2 + 1 3 + 1 5 + 1 8 + = ψ .
1 1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + .
1 1 + 1 4 + 1 9 + 1 16 + 1 25 + 1 36 + = π 2 6 .

Doc 10
0.3309
0.3309
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
ln 2 = 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - .

Doc 11
0.2949
0.2949
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Fraction_(mathematics).html
2 3 - 1 2 = 4 6 - 3 6 = 1 6

Doc 12
0.2922
0.2922
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Conditional_convergence.html
1 - 1 2 + 1 3 - 1 4 + 1 5 - = n = 1 ( - 1 ) n + 1 n

Doc 13
0.2893
0.7125
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
n = 0 ( ( - 1 ) n 2 n + 1 ) 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 - = arctan 1 = π 4
n = 0 ( ( - 1 ) n 2 n + 1 ) 3 = 1 1 3 - 1 3 3 + 1 5 3 - 1 7 3 + = π 3 32
n = 0 ( ( - 1 ) n 2 n + 1 ) 5 = 1 1 5 - 1 3 5 + 1 5 5 - 1 7 5 + = 5 π 5 1536
Doc 14
0.2892
0.7338
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Indian_mathematics.html
π 4 = 1 - 1 3 + 1 5 - 1 7 +
π 4 = 3 4 + 1 3 3 - 3 - 1 5 3 - 5 + 1 7 3 - 7 -
cos x = 1 - x 2 2 ! + x 4 4 ! - x 6 6 ! +
Doc 15
0.2873
0.2873
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Van_Wijngaarden_transformation.html
1 - 1 3 + 1 5 - 1 7 + = π 4 = 0.7853981

Doc 16
0.2672
0.2672
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Geometric_progression.html
1 2 - 1 4 + 1 8 - 1 16 + = 1 / 2 1 - ( - 1 / 2 ) = 1 3 .

Doc 17
0.2582
0.2582
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Cahen's_constant.html
C = ( - 1 ) i s i - 1 = 1 1 - 1 2 + 1 6 - 1 42 + 1 1806 - 0.64341054629.

Doc 18
0.2569
0.2569
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1_−_2_+_4_−_8_+_⋯.html
a 0 2 - Δ a 0 4 + Δ 2 a 0 8 - Δ 3 a 0 16 + = 1 2 - 1 4 + 1 8 - 1 16 + .

Doc 19
0.2523
0.6969
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Kerala_school_of_astronomy_and_mathematics.html
π 4 = 1 - 1 3 + 1 5 - 1 7 +
π 4 = 3 4 + 1 3 3 - 3 - 1 5 3 - 5 + 1 7 3 - 7 -
cos x = 1 - x 2 2 ! + x 4 4 ! - x 6 6 ! +
Doc 20
0.2500
0.6173
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pi.html
π = 4 1 - 4 3 + 4 5 - 4 7 + 4 9 - 4 11 + 4 13 -
π = 4 1 - 4 3 + 4 5 - 4 7 + 4 9 - 4 11 + 4 13 .
π 2 6 = 1 1 2 + 1 2 2 + 1 3 2 + 1 4 2 +
Doc 21
0.2375
0.6567
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Alternating_series.html
( 1 - 1 2 ) - 1 4 + ( 1 3 - 1 6 ) - 1 8 + ( 1 5 - 1 10 ) - 1 12 +
ln ( 2 ) = n = 1 ( - 1 ) n + 1 n = 1 - 1 2 + 1 3 - 1 4 + .
η ( s ) = n = 1 ( - 1 ) n - 1 n s = 1 1 s - 1 2 s + 1 3 s - 1 4 s +
Doc 22
0.2371
0.2371
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Biexciton.html
V = 2 ( 1 r 12 - 1 r 1 a - 1 r 1 b - 1 r 2 a - 1 r 2 b + 1 r a b )

Doc 23
0.2333
0.2333
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/List_of_definite_integrals.html
0 x e x + 1 d x = 1 1 2 - 1 2 2 + 1 3 2 - 1 4 2 + = π 2 12

Doc 24
0.2331
0.2331
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Yuktibhāṣā.html
π 4 = 1 - 1 3 + 1 5 - 1 7 + + ( - 1 ) n 2 n + 1 +

Doc 25
0.2331
0.2331
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Madhava_of_Sangamagrama.html
π 4 = 1 - 1 3 + 1 5 - 1 7 + + ( - 1 ) n 2 n + 1 +

Doc 26
0.2260
0.2260
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Mass_point_geometry.html
O 1 O 2 B E = B E - B O 2 - E O 1 B E = 1 - B O 2 B E - E O 1 B E = 1 - 1 2 - 3 13 = 7 26 .

Doc 27
0.2222
0.2222
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sylvester's_sequence.html
1 = 1 2 + 1 3 + 1 7 + 1 43 + 1 1807 + .

Doc 28
0.2173
0.2173
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/File:GeometricSegment.png.html
1 2 + 1 4 + 1 8 + 1 16 + = 1

Doc 29
0.2145
0.2145
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Kepler's_laws_of_planetary_motion.html
1 r min - 1 p = 1 p - 1 r max

Doc 30
0.2130
0.2130
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/2_(number).html
k = 0 1 2 k = 1 + 1 2 + 1 4 + 1 8 + 1 16 + = 2.

Doc 31
0.2128
0.2128
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Logarithmic_growth.html
1 + 1 2 + 1 3 + 1 4 + 1 5 +

Doc 32
0.2090
0.2090
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Summation_of_Grandi's_series.html
1 - x + x 2 2 ! - x 3 3 ! + x 4 4 ! - = e - x

Doc 33
0.2058
0.2058
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Generalized_continued_fraction.html
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 34
0.2053
0.2053
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_eta_function.html
η ( s ) = n = 1 ( - 1 ) n - 1 n s = 1 1 s - 1 2 s + 1 3 s - 1 4 s +

Doc 35
0.2005
0.2005
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Expected_value.html
i = 1 x i p i = c ( 1 - 1 2 + 1 3 - 1 4 + )

Doc 36
0.1981
0.1981
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Gauss's_continued_fraction.html
π 4 = 1 1 + 1 2 2 + 3 2 2 + 5 2 2 + = 1 - 1 3 + 1 5 - 1 7 + -

Doc 37
0.1979
0.1979
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1_−_2_+_3_−_4_+_⋯.html
1 2 a 0 - 1 4 Δ a 0 + 1 8 Δ 2 a 0 - = 1 2 - 1 4 .

Doc 38
0.1975
0.1975
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Irrationality_sequence.html
1 2 + 1 3 + 1 7 + 1 43 + = 1 ,

Doc 39
0.1973
0.1973
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Partial_fraction_decomposition.html
1 18 = 1 2 - 1 3 - 1 3 2 .

Doc 40
0.1931
0.1931
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_trial.html
q = 1 - p = 1 - 1 2 = 1 2

Doc 41
0.1892
0.3644
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Taylor_series.html
- x - 1 2 x 2 - 1 3 x 3 - 1 4 x 4 -
cos x = 1 - x 2 2 ! + x 4 4 ! -

Doc 42
0.1878
0.1878
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/William_Brouncker,_2nd_Viscount_Brouncker.html
1 1 + 1 2 2 + 3 2 2 = 13 15 = 1 - 1 3 + 1 5 .

Doc 43
0.1864
0.3570
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Euler_product.html
π / 4 = n = 0 ( - 1 ) n 2 n + 1 = 1 - 1 3 + 1 5 - 1 7 + ,
p ( 1 - 3 p 3 + 2 p 4 + 1 p 5 - 1 p 6 ) = 0.678234...

Doc 44
0.1853
0.1853
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Prime_zeta_function.html
1 2 + 1 3 + 1 5 + 1 7 + 1 11 + .

Doc 45
0.1818
0.1818
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Greedy_algorithm_for_Egyptian_fractions.html
φ = 1 1 + 1 2 + 1 9 + 1 145 + 1 37986 +

Doc 46
0.1818
0.1818
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Divergent_series.html
1 + 1 2 + 1 3 + 1 4 + 1 5 + = n = 1 1 n .

Doc 47
0.1807
0.3590
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Egyptian_fraction.html
8 11 = 1 2 + 1 22 + 1 6 + 1 66 .
5 12 = 1 4 + 1 10 + 1 15 = 1 5 + 1 6 + 1 20 .

Doc 48
0.1807
0.1807
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Genetic_drift.html
1 2 1 2 1 2 1 2 = 1 16 .

Doc 49
0.1801
0.1801
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Random_permutation_statistics.html
n ! ( 1 - 1 1 ! + 1 2 ! - 1 3 ! + ± 1 n ! ) = n ! k = 0 n ( - 1 ) k k !

Doc 50
0.1795
0.7179
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1 50 + 1 30 + 1 150 + 1 400 = 1 16
1 50 + 1 30 + 1 150 + 1 400 = 1 16
1 25 + 1 15 + 1 75 + 1 200 = 1 8
1 25 + 1 15 + 1 75 + 1 200 = 1 8

Doc 51
0.1771
0.1771
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Smith–Volterra–Cantor_set.html
n = 0 2 n 2 2 n + 2 = 1 4 + 1 8 + 1 16 + = 1 2

Doc 52
0.1766
0.1766
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Divergence_of_the_sum_of_the_reciprocals_of_the_primes.html
n = 1 1 n = 1 + 1 2 + 1 3 + 1 4 +

Doc 53
0.1726
0.1726
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Rhind_Mathematical_Papyrus_2::n_table.html
2 n = 1 n + 1 2 n + 1 3 n + 1 6 n

Doc 54
0.1703
0.1703
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Net_run_rate.html
254 147.333 + 199 147.333 + 225 147.333 - 253 150 - 110 150 - 103 150 .

Doc 55
0.1702
0.1702
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Cours_d'Analyse.html
1 4 , 1 3 , 1 6 , 1 5 , 1 8 , 1 7 ,