Returned 76 matches (100 formulae, 67 docs)
    Lookup 170.162 ms, Re-ranking 3336.376 ms
    Found 258025 tuple postings, 77679 formulae, 14745 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
0.6724
1.0554
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Fraction_(mathematics).html
2 3 - 1 2 = 4 6 - 3 6 = 1 6
1 3 + 1 4 + 1 6 + 1 68

Doc 2
0.6280
0.6280
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 3
0.5889
0.5889
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 4
0.5748
0.5748
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Partial_fraction_decomposition.html
1 18 = 1 2 - 1 3 - 1 3 2 .

Doc 5
0.5656
0.5656
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
k = 0 1 16 k ( 4 8 k + 1 - 2 8 k + 4 - 1 8 k + 5 - 1 8 k + 6 ) = π

Doc 6
0.5590
0.9719
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
1 1 - 1 2 + 1 3 - 1 4 + 1 5 = ln ( 2 )
1 1 - 1 2 + 1 4 - 1 8 + 1 16 - 1 32 + = 2 3 .

Doc 7
0.5576
1.0175
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Indian_mathematics.html
π 4 = 3 4 + 1 3 3 - 3 - 1 5 3 - 5 + 1 7 3 - 7 -
π 4 = 1 - 1 3 + 1 5 - 1 7 +

Doc 8
0.5576
1.0175
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Kerala_school_of_astronomy_and_mathematics.html
π 4 = 3 4 + 1 3 3 - 3 - 1 5 3 - 5 + 1 7 3 - 7 -
π 4 = 1 - 1 3 + 1 5 - 1 7 +

Doc 9
0.5541
0.9790
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
1 2 = 1 3 + 1 9 + 1 27 + 1 81 +

Doc 10
0.5125
0.5125
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Vertical_electrical_sounding.html
k = 2 π 1 r A M - 1 r B M - 1 r A N + 1 r B N

Doc 11
0.5119
0.5119
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Bicentric_quadrilateral.html
1 I A 2 + 1 I C 2 = 1 I B 2 + 1 I D 2 = 1 r 2

Doc 12
0.5100
0.5100
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Phonon_scattering.html
1 τ C = 1 τ U + 1 τ M + 1 τ B + 1 τ p h - e

Doc 13
0.4974
0.4974
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Optic_equation.html
1 I A 2 + 1 I C 2 = 1 I B 2 + 1 I D 2 = 1 r 2 .

Doc 14
0.4925
0.9351
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Egyptian_fraction.html
1 k + 1 k = 1 k + 1 k + 1 + 1 k ( k + 1 ) .
8 11 = 1 2 + 1 22 + 1 6 + 1 66 .

Doc 15
0.4852
0.4852
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Scheimpflug_principle.html
1 u + 1 v = 1 u cos θ + 1 v cos θ = 1 f .

Doc 16
0.4821
0.4821
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 17
0.4798
0.4798
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Proof_that_22::7_exceeds_π.html
22 7 - 1 630 < π < 22 7 - 1 1260 ,

Doc 18
0.4713
8.0127
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
1 22 + 1 33 + 1 66 = 1 11
1 22 + 1 33 + 1 66 = 1 11
1 28 + 1 49 + 1 196 = 1 13
1 28 + 1 49 + 1 196 = 1 13
1 30 + 1 45 + 1 90 = 1 15
1 30 + 1 45 + 1 90 = 1 15
1 6 + 1 6 + 1 6 = 1 2
1 6 + 1 6 + 1 6 = 1 2
1 7 + 1 14 + 1 28 = 1 4
1 7 + 1 14 + 1 28 = 1 4
1 25 + 1 50 + 1 150 = 1 6
1 25 + 1 50 + 1 150 = 1 6
1 14 + 1 21 + 1 42 = 1 7
1 14 + 1 21 + 1 42 = 1 7
1 18 + 1 27 + 1 54 = 1 9
1 18 + 1 27 + 1 54 = 1 9

Doc 19
0.4689
0.4689
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 20
0.4680
0.4680
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Tetrahedron.html
1 r 1 2 + 1 r 2 2 + 1 r 3 2 + 1 r 4 2 2 r 2 ,

Doc 21
0.4655
0.4655
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Ancient_Egyptian_multiplication.html
26 97 = 1 4 + 1 97 + 1 194 + 1 388

Doc 22
0.4585
0.4585
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 .

Doc 23
0.4481
0.4481
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Genetic_drift.html
1 2 1 2 1 2 1 2 = 1 16 .

Doc 24
0.4445
0.4445
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Hölder's_inequality.html
k = 1 n - 1 1 p k = 1 r - 1 p n = p n - r r p n = 1 p r ,

Doc 25
0.4425
0.4425
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Greedy_algorithm_for_Egyptian_fractions.html
1 2 + 1 3 + 1 7 + 1 43 = 1805 1806

Doc 26
0.4425
0.8344
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 .
254 97.333 + 199 97.333 - 253 100 - 110 100 .

Doc 27
0.4414
2.7191
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
k = 1 ( - 1 ) k s k - 1 = 1 1 - 1 2 + 1 6 - 1 42 + 1 1806 ±
n = 0 ( - 1 ) n n ! = 1 0 ! - 1 1 ! + 1 2 ! - 1 3 ! + 1 4 ! - 1 5 ! +
n = 1 ( - 1 ) n + 1 n ! = 1 1 ! - 1 2 ! + 1 3 ! - 1 4 ! + 1 5 ! - 1 6 ! +
3 3 4 ( 1 - 1 2 2 + 1 4 2 - 1 5 2 + 1 7 2 - 1 8 2 + 1 10 2 ± )
π 4 = n = 0 ( - 1 ) n 2 n + 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 -
n = 1 1 n ( 2 n n ) = 1 - 1 2 + 1 4 - 1 5 + 1 7 - 1 8 +
n = 1 ( - 1 ) n - 1 2 2 n + 1 = 1 1 + 1 3 - 1 5 - 1 7 + 1 9 + 1 11 -

Doc 28
0.4390
0.8364
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Quantum_cascade_laser.html
d n 2 d t = n 3 τ 32 + n 1 τ 12 - n 2 τ 21 - n 2 τ 23
d n 1 d t = n 2 τ 21 + n 3 τ 31 - n 1 τ 13 - n 1 τ 12 - I out

Doc 29
0.4355
0.4355
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Euler_product.html
p ( 1 - 3 p 3 + 2 p 4 + 1 p 5 - 1 p 6 ) = 0.678234...

Doc 30
0.4229
0.7645
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 -

Doc 31
0.4112
0.4112
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Correspondence_principle.html
n = E ω - 1 2 = m ω A 2 2 - 1 2

Doc 32
0.4056
1.2090
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Orthodiagonal_quadrilateral.html
1 h 1 2 + 1 h 3 2 = 1 h 2 2 + 1 h 4 2
1 h 1 2 + 1 h 3 2 = 1 h 2 2 + 1 h 4 2
1 h 1 + 1 h 3 = 1 h 2 + 1 h 4
Doc 33
0.4038
0.4038
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Drawing_straws.html
N - 1 N × N - 2 N - 1 × N - 3 N - 2 × 1 N - 3 = 1 N

Doc 34
0.4026
0.7606
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Riemann_series_theorem.html
1 - 1 2 + 1 3 - 1 4 +
1 - 1 2 - 1 4 + 1 3 - 1 6 - 1 8 + 1 5 - 1 10 - 1 12 +

Doc 35
0.4020
0.4020
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Linkage_disequilibrium.html
1 w = 1 a + 1 b + 1 c + 1 d ( = 0.0703 )

Doc 36
0.4014
0.4014
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Water_hammer.html
1 B 𝑒𝑓𝑓 = 1 B l + 1 B e q + 1 B g

Doc 37
0.4011
0.4011
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sylvester's_sequence.html
1 s i - 1 - 1 s i + 1 - 1 = 1 s i ,

Doc 38
0.3978
1.1935
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Ex-tangential_quadrilateral.html
1 h 1 + 1 h 4 = 1 h 2 + 1 h 3
1 h 1 + 1 h 3 = 1 h 2 + 1 h 4
1 h 1 + 1 h 2 = 1 h 3 + 1 h 4
Doc 39
0.3966
0.3966
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Draft:Leaving_Certificate_Mathematics_Ordinary_Level.html
1 2 - 1 4 = 1 4

Doc 40
0.3946
0.3946
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Triangle.html
1 r = 1 h a + 1 h b + 1 h c

Doc 41
0.3930
0.3930
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Soddy's_hexlet.html
1 r 1 + 1 r 4 = 1 r 2 + 1 r 5 = 1 r 3 + 1 r 6 .

Doc 42
0.3848
1.5391
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Tangential_quadrilateral.html
1 R a + 1 R c = 1 R b + 1 R d .
1 h 1 + 1 h 3 = 1 h 2 + 1 h 4 .
1 r 1 + 1 r 3 = 1 r 2 + 1 r 4 .
1 r a + 1 r c = 1 r b + 1 r d .

Doc 43
0.3823
0.3823
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Ray_transfer_matrix_analysis.html
1 q 2 = - q 1 f + 1 q 1 = 1 q 1 - 1 f

Doc 44
0.3814
0.3814
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Half-life.html
1 T 1 2 = 1 t 1 + 1 t 2 + 1 t 3 +

Doc 45
0.3811
0.3811
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Altitude_(triangle).html
1 r = 1 h a + 1 h b + 1 h c .

Doc 46
0.3794
0.3794
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 47
0.3794
0.3794
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 48
0.3764
0.7529
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Smith_chart.html
1 Y T S = 1 Y 1 + 1 Y 2 + 1 Y 3 +
1 Z T P = 1 Z 1 + 1 Z 2 + 1 Z 3 +

Doc 49
0.3761
0.3761
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Mean.html
5 1 4 + 1 36 + 1 45 + 1 50 + 1 75 = 5 1 3 = 15.

Doc 50
0.3709
0.3709
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Factorial.html
- ζ ( 3 ) 3 - π 2 γ 12 - γ 3 6

Doc 51
0.3709
0.3709
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Large_set_(combinatorics).html
1 s 0 + 1 s 1 + 1 s 2 + 1 s 3 +

Doc 52
0.3700
0.3700
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Orbital_period.html
1 P s y n = 1 P 1 - 1 P 2

Doc 53
0.3668
0.7335
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Electron_mobility.html
1 μ = 1 μ impurities + 1 μ lattice + 1 μ defects +
1 τ = 1 τ impurities + 1 τ lattice + 1 τ defects +

Doc 54
0.3659
0.3659
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pendulum.html
1 Δ T = 1 T 1 - 1 T 2

Doc 55
0.3611
1.4442
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Series_and_parallel_circuits.html
1 C total = 1 C 1 + 1 C 2 + + 1 C n
1 G total = 1 G 1 + 1 G 2 + + 1 G n
1 L total = 1 L 1 + 1 L 2 + + 1 L n
1 R total = 1 R 1 + 1 R 2 + + 1 R n

Doc 56
0.3611
0.3611
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Electrical_impedance.html
1 Z eq = 1 Z 1 + 1 Z 2 + + 1 Z n

Doc 57
0.3611
0.3611
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Inductor.html
1 L eq = 1 L 1 + 1 L 2 + + 1 L n

Doc 58
0.3611
0.3611
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Capacitor.html
1 C eq = 1 C 1 + 1 C 2 + + 1 C n

Doc 59
0.3563
0.3563
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Current_divider.html
1 R T = 1 R 1 + 1 R 2 + 1 R 3 + .

Doc 60
0.3504
0.3504
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sobolev_inequality.html
1 p * = 1 p - 1 n .

Doc 61
0.3464
0.3464
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/History_of_Grandi's_series.html
k 2 m = k m - k m + k m - .

Doc 62
0.3419
0.3419
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/James_Meade.html
U S . Y K = 1 10 × 1 10 × 1 2 = 1 2

Doc 63
0.3416
0.3416
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 -

Doc 64
0.3373
0.3373
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 65
0.2924
0.2924
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Practical_number.html
13 20 = 10 20 + 2 20 + 1 20 = 1 2 + 1 10 + 1 20 .

Doc 66
0.2654
0.2654
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Marshall–Lerner_condition.html
N x e 1 X = X e 1 X - 1 Q Q e - 1 e

Doc 67
0.1845
0.1845
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 + .