Returned 97 matches (100 formulae, 55 docs)
    Lookup 16.844 ms, Re-ranking 1051.077 ms
    Found 222920 tuple postings, 88494 formulae, 15993 documents
[ formulas ] [ documents ] [ documents-by-formula ]

x - 1 - 1 2 - 1 4 - 1 5 - 1 6 - 1 9 - = 1
Doc 1
1.0000, 0.0000, 27.0000, 3.7824
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
1 - 1 2 - 1 4 + 1 3 - 1 6 - 1 8 + 1 5 - 1 10 - 1 12 +
Doc 2
0.7157, -15.0000, 18.0000, 2.7927
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Riemann_series_theorem.html
n = 0 ( ( - 1 ) n 2 n + 1 ) 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 - = arctan 1 = π 4
Doc 3
0.6946, -25.0000, 17.0000, 1.7793
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
ln 2 = 1 1 - 1 2 + 1 3 - 1 4 + 1 5 - .
Doc 4
0.6723, -5.0000, 14.0000, 0.6723
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
1 1 - 1 2 + 1 4 - 1 8 + 1 16 - 1 32 + = 2 3 .
Doc 5
0.6723, -10.0000, 17.0000, 4.3284
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
π = 4 1 - 4 3 + 4 5 - 4 7 + 4 9 - 4 11 + 4 13 -
Doc 6
0.6723, -11.0000, 10.0000, 1.7328
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pi.html
n = 1 1 n ( 2 n n ) = 1 - 1 2 + 1 4 - 1 5 + 1 7 - 1 8 +
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.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 8
0.6723, -33.0000, 13.0000, 0.6723
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Generalized_continued_fraction.html
C = ( - 1 ) i s i - 1 = 1 1 - 1 2 + 1 6 - 1 42 + 1 1806 - 0.64341054629.
Doc 9
0.6566, -17.0000, 14.0000, 0.6566
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Cahen's_constant.html
3 3 4 ( 1 - 1 2 2 + 1 4 2 - 1 5 2 + 1 7 2 - 1 8 2 + 1 10 2 ± )
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
π 4 = n = 0 ( - 1 ) n 2 n + 1 = 1 1 - 1 3 + 1 5 - 1 7 + 1 9 -
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
n = 1 ( - 1 ) n - 1 2 2 n + 1 = 1 1 + 1 3 - 1 5 - 1 7 + 1 9 + 1 11 -
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
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 -
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
π = 4 1 - 4 3 + 4 5 - 4 7 + 4 9 - 4 11 + 4 13 .
Doc 6
0.6723, -11.0000, 10.0000, 1.7328
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pi.html
n = 0 ( - 1 ) n n ! = 1 0 ! - 1 1 ! + 1 2 ! - 1 3 ! + 1 4 ! - 1 5 ! +
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
n = 1 ( - 1 ) n + 1 n ! = 1 1 ! - 1 2 ! + 1 3 ! - 1 4 ! + 1 5 ! - 1 6 ! +
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
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 ±
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
1 2 - 1 4 + 1 6 - 1 8 + 1 10 + + 1 2 ( 2 k - 1 ) - 1 2 ( 2 k ) +
Doc 2
0.7157, -15.0000, 18.0000, 2.7927
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Riemann_series_theorem.html
2 3 - 1 2 = 4 6 - 3 6 = 1 6
Doc 10
0.5805, -2.0000, 10.0000, 0.5805
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Fraction_(mathematics).html
1 - 1 2 + 1 3 - 1 4 + 1 5 - = ln 2.
Doc 11
0.5805, -5.0000, 13.0000, 2.8206
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_series_(mathematics).html
1 - 1 3 + 1 5 - 1 7 + 1 9 - = π 4 ,
Doc 12
0.5805, -7.0000, 15.0000, 0.5805
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 13
0.5805, -7.0000, 15.0000, 0.5805
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Leibniz_formula_for_π.html
1 - 1 2 - 1 4 + 1 8 - 1 16 + = 1 3 .
Doc 14
0.5805, -7.0000, 13.0000, 1.1229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1::2_−_1::4_+_1::8_−_1::16_+_⋯.html
1 1 - 1 2 + 1 3 - 1 4 + 1 5 = ln ( 2 )
Doc 5
0.6723, -10.0000, 17.0000, 4.3284
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
1 - 1 2 + 1 3 - 1 4 + 1 5 - = n = 1 ( - 1 ) n + 1 n
Doc 15
0.5805, -16.0000, 13.0000, 0.5805
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 1 n = ln ( 2 ) .
Doc 16
0.5805, -22.0000, 13.0000, 1.9242
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
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 -
Doc 2
0.7157, -15.0000, 18.0000, 2.7927
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Riemann_series_theorem.html
π 4 = 3 4 + 1 3 3 - 3 - 1 5 3 - 5 + 1 7 3 - 7 -
Doc 17
0.5574, -13.0000, 12.0000, 1.3108
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Kerala_school_of_astronomy_and_mathematics.html
Doc 18
0.5574, -13.0000, 12.0000, 1.3108
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Indian_mathematics.html
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
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
1 1 + 1 2 + 1 4 + 1 8 + 1 16 + 1 32 + = 2.
Doc 5
0.6723, -10.0000, 17.0000, 4.3284
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
1 1 + 1 3 + 1 6 + 1 10 + 1 15 + 1 21 + = 2.
Doc 5
0.6723, -10.0000, 17.0000, 4.3284
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
n = 1 ( - 1 ) n + 1 n = 1 - 1 2 + 1 3 - 1 4 + 1 5 -
Doc 11
0.5805, -5.0000, 13.0000, 2.8206
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_series_(mathematics).html
Doc 16
0.5805, -22.0000, 13.0000, 1.9242
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
1 2 - 1 4 + 1 8 - 1 16 + = 1 / 2 1 - ( - 1 / 2 ) = 1 3 .
Doc 14
0.5805, -7.0000, 13.0000, 1.1229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1::2_−_1::4_+_1::8_−_1::16_+_⋯.html
Doc 19
0.5424, -18.0000, 12.0000, 0.5424
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Geometric_progression.html
0 x e x + 1 d x = 1 1 2 - 1 2 2 + 1 3 2 - 1 4 2 + = π 2 12
Doc 20
0.5424, -22.0000, 11.0000, 0.5424
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/List_of_definite_integrals.html
n = 0 ( ( - 1 ) n 2 n + 1 ) 3 = 1 1 3 - 1 3 3 + 1 5 3 - 1 7 3 + = π 3 32
Doc 3
0.6946, -25.0000, 17.0000, 1.7793
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
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 3
0.6946, -25.0000, 17.0000, 1.7793
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
η ( s ) = n = 1 ( - 1 ) n - 1 n s = 1 1 s - 1 2 s + 1 3 s - 1 4 s +
Doc 21
0.5326, -23.0000, 12.0000, 1.3505
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Alternating_series.html
Doc 22
0.5326, -23.0000, 12.0000, 0.5326
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_eta_function.html
x - 1 - 1 2 = 1 + 1 5 + 1 6 + 1 7 + 1 10 + 1 11 + 1 12 +
Doc 1
1.0000, 0.0000, 27.0000, 3.7824
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
n = 1 1 n 2 n = n = 1 ( - 1 ) n + 1 n = 1 1 - 1 2 + 1 3 - 1 4 +
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.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 23
0.5189, -29.0000, 12.0000, 0.5189
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1_−_2_+_4_−_8_+_⋯.html
π 3 32 = n = 1 - 1 n + 1 ( - 1 + 2 n ) 3 = 1 1 3 - 1 3 3 + 1 5 3 - 1 7 3 +
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.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 24
0.5091, -24.0000, 14.0000, 0.5091
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Biexciton.html
1 1 + 1 1 + 1 2 + 1 6 + 1 24 + 1 120 + = e .
Doc 5
0.6723, -10.0000, 17.0000, 4.3284
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
1 1 + 1 1 + 1 2 + 1 3 + 1 5 + 1 8 + = ψ .
Doc 5
0.6723, -10.0000, 17.0000, 4.3284
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
1 1 + 1 4 + 1 9 + 1 16 + 1 25 + 1 36 + = π 2 6 .
Doc 5
0.6723, -10.0000, 17.0000, 4.3284
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
n = 1 1 n 3 = 1 1 3 + 1 2 3 + 1 3 3 + 1 4 3 + 1 5 3 + =
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
= 1 π ( 1 2 - 1 3 2 3 + 1 5 2 5 - 1 7 2 7 + )
Doc 7
0.6723, -16.0000, 18.0000, 7.7679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
1 18 = 1 2 - 1 3 - 1 3 2 .
Doc 25
0.4884, -3.0000, 10.0000, 0.4884
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Partial_fraction_decomposition.html
1 2 k - 1 - 1 2 ( 2 k - 1 ) - 1 4 k , k = 1 , 2 , .
Doc 2
0.7157, -15.0000, 18.0000, 2.7927
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Riemann_series_theorem.html
π 4 = 1 - 1 3 + 1 5 - 1 7 + + ( - 1 ) n 2 n + 1 +
Doc 26
0.4803, -16.0000, 11.0000, 0.4803
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Yuktibhāṣā.html
Doc 27
0.4803, -16.0000, 11.0000, 0.4803
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Madhava_of_Sangamagrama.html
n = 0 ( - 1 ) n 2 n + 1 = 1 - 1 3 + 1 5 - 1 7 + = π 4 .
Doc 11
0.5805, -5.0000, 13.0000, 2.8206
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_series_(mathematics).html
1 = 1 2 + 1 3 + 1 7 + 1 43 + 1 1807 + .
Doc 28
0.4775, -7.0000, 13.0000, 0.4775
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sylvester's_sequence.html
x - 1 = 1 + 1 2 + 1 4 + 1 5 + 1 6 + 1 9 +
Doc 1
1.0000, 0.0000, 27.0000, 3.7824
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
x = 1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + 1 7 + 1 8
Doc 1
1.0000, 0.0000, 27.0000, 3.7824
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
1 2 = 1 3 + 1 9 + 1 27 + 1 81 +
Doc 1
1.0000, 0.0000, 27.0000, 3.7824
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
φ = 1 1 + 1 2 + 1 9 + 1 145 + 1 37986 +
Doc 29
0.4665, -7.0000, 11.0000, 0.4665
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Greedy_algorithm_for_Egyptian_fractions.html
1 2 + 1 3 + 1 5 + 1 7 + 1 11 + .
Doc 30
0.4665, -8.0000, 13.0000, 0.4665
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Prime_zeta_function.html
1 4 , 1 3 , 1 6 , 1 5 , 1 8 , 1 7 ,
Doc 31
0.4665, -9.0000, 11.0000, 0.4665
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Cours_d'Analyse.html
1 1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + .
Doc 5
0.6723, -10.0000, 17.0000, 4.3284
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
x - 1 = 1 + 1 3 + 1 5 + 1 6 + 1 7 + 1 9 + 1 10 + 1 11 +
Doc 1
1.0000, 0.0000, 27.0000, 3.7824
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
1 + 1 2 + 1 3 + 1 4 + 1 5 + 1 6 + 1 7 + 1 8 + 1 9 +
Doc 11
0.5805, -5.0000, 13.0000, 2.8206
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_series_(mathematics).html
1 - 1 3 + 1 5 - 1 7 + = π 4 = 0.7853981
Doc 32
0.4660, -8.0000, 10.0000, 0.4660
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Van_Wijngaarden_transformation.html
n ! ( 1 - 1 1 ! + 1 2 ! - 1 3 ! + ± 1 n ! ) = n ! k = 0 n ( - 1 ) k k !
Doc 33
0.4660, -27.0000, 11.0000, 0.4660
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Random_permutation_statistics.html
π 4 = 1 1 + 1 2 2 + 3 2 2 + 5 2 2 + = 1 - 1 3 + 1 5 - 1 7 + -
Doc 34
0.4660, -27.0000, 10.0000, 0.4660
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Gauss's_continued_fraction.html
1 2 + 1 4 + 1 8 + 1 16 + = 1
Doc 35
0.4545, -4.0000, 11.0000, 0.4545
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/File:GeometricSegment.png.html
1 50 + 1 30 + 1 150 + 1 400 = 1 16
Doc 36
0.4545, -4.0000, 10.0000, 1.8182
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 36
0.4545, -4.0000, 10.0000, 1.8182
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1 25 + 1 15 + 1 75 + 1 200 = 1 8
Doc 36
0.4545, -4.0000, 10.0000, 1.8182
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 36
0.4545, -4.0000, 10.0000, 1.8182
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1 2 1 2 1 2 1 2 = 1 16 .
Doc 38
0.4545, -5.0000, 11.0000, 0.4545
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Genetic_drift.html
1 2 + 1 3 + 1 7 + 1 43 + = 1 ,
Doc 37
0.4545, -5.0000, 11.0000, 0.4545
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Irrationality_sequence.html
8 11 = 1 2 + 1 22 + 1 6 + 1 66 .
Doc 39
0.4545, -5.0000, 10.0000, 0.9091
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Egyptian_fraction.html
5 12 = 1 4 + 1 10 + 1 15 = 1 5 + 1 6 + 1 20 .
Doc 39
0.4545, -5.0000, 10.0000, 0.9091
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Egyptian_fraction.html
k = 0 1 2 k = 1 + 1 2 + 1 4 + 1 8 + 1 16 + = 2.
Doc 40
0.4545, -16.0000, 10.0000, 0.4545
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/2_(number).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 41
0.4504, -39.0000, 10.0000, 0.4504
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Mass_point_geometry.html
π 4 = 1 - 1 3 + 1 5 - 1 7 +
Doc 18
0.5574, -13.0000, 12.0000, 1.3108
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Indian_mathematics.html
π 4 = 1 - 1 3 + 1 5 - 1 7 +
Doc 17
0.5574, -13.0000, 12.0000, 1.3108
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Kerala_school_of_astronomy_and_mathematics.html
π / 4 = n = 0 ( - 1 ) n 2 n + 1 = 1 - 1 3 + 1 5 - 1 7 + ,
Doc 42
0.4416, -21.0000, 11.0000, 0.7922
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Euler_product.html
π 2 6 = 1 1 2 + 1 2 2 + 1 3 2 + 1 4 2 +
Doc 6
0.6723, -11.0000, 10.0000, 1.7328
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pi.html
1 + 1 2 + 1 3 + 1 4 + 1 5 + = n = 1 1 n .
Doc 16
0.5805, -22.0000, 13.0000, 1.9242
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
Doc 43
0.4152, -15.0000, 10.0000, 0.4152
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Divergent_series.html
n = 0 2 n 2 2 n + 2 = 1 4 + 1 8 + 1 16 + = 1 2
Doc 44
0.4152, -17.0000, 9.0000, 0.4152
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Smith–Volterra–Cantor_set.html
ln ( 2 ) = n = 1 ( - 1 ) n + 1 n = 1 - 1 2 + 1 3 - 1 4 + .
Doc 21
0.5326, -23.0000, 12.0000, 1.3505
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Alternating_series.html
1 - 1 2 + 1 3 - 1 4 +
Doc 2
0.7157, -15.0000, 18.0000, 2.7927
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Riemann_series_theorem.html
i = 1 x i p i = c ( 1 - 1 2 + 1 3 - 1 4 + )
Doc 45
0.4124, -15.0000, 10.0000, 0.4124
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Expected_value.html
1 1 + 1 2 2 + 3 2 2 = 13 15 = 1 - 1 3 + 1 5 .
Doc 46
0.4028, -15.0000, 8.0000, 0.4028
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/William_Brouncker,_2nd_Viscount_Brouncker.html
( 1 - 1 2 ) - 1 4 + ( 1 3 - 1 6 ) - 1 8 + ( 1 5 - 1 10 ) - 1 12 +
Doc 21
0.5326, -23.0000, 12.0000, 1.3505
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Alternating_series.html
1 + 1 2 + 1 4 + 1 8 + + 1 2 n + .
Doc 16
0.5805, -22.0000, 13.0000, 1.9242
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
1 = 1 2 + 1 4 + 1 8 + 1 16 +
Doc 1
1.0000, 0.0000, 27.0000, 3.7824
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
1 + 1 2 + 1 3 + 1 4 + 1 5 +
Doc 47
0.3755, -6.0000, 10.0000, 0.3755
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Logarithmic_growth.html
2 n = 1 n + 1 2 n + 1 3 n + 1 6 n
Doc 48
0.3755, -9.0000, 9.0000, 0.3755
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Rhind_Mathematical_Papyrus_2::n_table.html
area of rectangles = 1 + 1 2 + 1 3 + 1 4 + 1 5 + .
Doc 11
0.5805, -5.0000, 13.0000, 2.8206
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_series_(mathematics).html
n = 1 1 n = 1 + 1 2 + 1 3 + 1 4 + 1 5 + .
Doc 11
0.5805, -5.0000, 13.0000, 2.8206
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_series_(mathematics).html
p ( 1 - 3 p 3 + 2 p 4 + 1 p 5 - 1 p 6 ) = 0.678234...
Doc 42
0.4416, -21.0000, 11.0000, 0.7922
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Euler_product.html
1 - x + x 2 2 ! - x 3 3 ! + x 4 4 ! - = e - x
Doc 49
0.3506, -16.0000, 8.0000, 0.3506
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Summation_of_Grandi's_series.html
1 2 a 0 - 1 4 Δ a 0 + 1 8 Δ 2 a 0 - = 1 2 - 1 4 .
Doc 50
0.3506, -20.0000, 8.0000, 0.3506
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1_−_2_+_3_−_4_+_⋯.html
1 r min - 1 p = 1 p - 1 r max
Doc 51
0.3361, -7.0000, 10.0000, 0.3361
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Kepler's_laws_of_planetary_motion.html
n = 1 1 n = 1 + 1 2 + 1 3 + 1 4 +
Doc 52
0.3353, -12.0000, 9.0000, 0.3353
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Divergence_of_the_sum_of_the_reciprocals_of_the_primes.html
cos x = 1 - x 2 2 ! + x 4 4 ! - x 6 6 ! +
Doc 17
0.5574, -13.0000, 12.0000, 1.3108
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Kerala_school_of_astronomy_and_mathematics.html
Doc 18
0.5574, -13.0000, 12.0000, 1.3108
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Indian_mathematics.html
q = 1 - p = 1 - 1 2 = 1 2
Doc 53
0.2844, -5.0000, 7.0000, 0.2844
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_trial.html
- x - 1 2 x 2 - 1 3 x 3 - 1 4 x 4 -
Doc 54
0.2727, -13.0000, 8.0000, 0.5060
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Taylor_series.html
254 147.333 + 199 147.333 + 225 147.333 - 253 150 - 110 150 - 103 150 .
Doc 55
0.2595, -16.0000, 8.0000, 0.2595
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Net_run_rate.html
cos x = 1 - x 2 2 ! + x 4 4 ! -
Doc 54
0.2727, -13.0000, 8.0000, 0.5060
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Taylor_series.html