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Search
Returned 76 matches (100 formulae, 67 docs)
Lookup 170.162 ms, Re-ranking 2065.019 ms
Found 258025 tuple postings, 77679 formulae, 14745 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
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Doc 1
1.0000, -8.0000, 14.0000, 1.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
V
=
2
(
1
r
12
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r
1
a
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1
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1
r
2
a
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1
r
2
b
+
1
r
a
b
)
Doc 2
1.0000, -10.0000, 14.0000, 1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Biexciton.html
1
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1
2
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1
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1
10
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1
12
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⋯
Doc 3
0.9172, -17.0000, 13.0000, 1.4538
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 4
0.8322, -2.0000, 9.0000, 1.3539
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Fraction_(mathematics).html
1
1
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1
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1
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⋯
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ln
(
2
)
Doc 5
0.8322, -7.0000, 12.0000, 1.6643
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
ln
2
=
1
1
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1
3
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1
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1
5
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⋯
.
Doc 6
0.8322, -8.0000, 12.0000, 0.8322
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
1
1
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1
2
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1
4
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8
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1
16
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1
32
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⋯
=
2
3
.
Doc 5
0.8322, -7.0000, 12.0000, 1.6643
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
3
3
4
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1
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1
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2
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1
8
2
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1
10
2
±
⋯
)
Doc 7
0.8322, -17.0000, 12.0000, 5.8252
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
∑
n
=
1
∞
1
n
(
2
n
n
)
=
1
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2
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1
4
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1
7
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1
8
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⋯
Doc 7
0.8322, -17.0000, 12.0000, 5.8252
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
C
=
∑
(
-
1
)
i
s
i
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1
1
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1
6
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42
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1
1806
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⋯
≈
0.64341054629.
Doc 8
0.8322, -19.0000, 12.0000, 0.8322
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Cahen's_constant.html
∑
k
=
1
∞
(
-
1
)
k
s
k
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1
=
1
1
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1
2
+
1
6
-
1
42
+
1
1806
±
⋯
Doc 7
0.8322, -17.0000, 12.0000, 5.8252
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
∑
n
=
0
∞
(
-
1
)
n
n
!
=
1
0
!
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1
1
!
+
1
2
!
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1
3
!
+
1
4
!
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1
5
!
+
⋯
Doc 7
0.8322, -17.0000, 12.0000, 5.8252
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
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1
7
+
1
9
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⋯
Doc 7
0.8322, -17.0000, 12.0000, 5.8252
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
∑
n
=
1
∞
(
-
1
)
n
+
1
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!
=
1
1
!
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1
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!
+
1
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!
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1
4
!
+
1
5
!
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1
6
!
+
⋯
Doc 7
0.8322, -17.0000, 12.0000, 5.8252
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
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1
7
+
1
9
+
1
11
-
⋯
Doc 7
0.8322, -17.0000, 12.0000, 5.8252
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
∑
k
=
0
∞
1
16
k
(
4
8
k
+
1
-
2
8
k
+
4
-
1
8
k
+
5
-
1
8
k
+
6
)
=
π
Doc 9
0.7836, -12.0000, 9.0000, 0.7836
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
1
-
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2
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4
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8
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1
16
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⋯
=
1
3
.
Doc 10
0.7544, -9.0000, 11.0000, 0.7544
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1::2_−_1::4_+_1::8_−_1::16_+_⋯.html
1
r
min
-
1
p
=
1
p
-
1
r
max
Doc 11
0.7000, -1.0000, 10.0000, 0.7000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Kepler's_laws_of_planetary_motion.html
1
18
=
1
2
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1
3
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1
3
2
.
Doc 12
0.7000, -2.0000, 10.0000, 0.7000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Partial_fraction_decomposition.html
22
7
-
1
630
<
π
<
22
7
-
1
1260
,
Doc 13
0.7000, -4.0000, 8.0000, 0.7000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Proof_that_22::7_exceeds_π.html
k
=
2
π
1
r
A
M
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1
r
B
M
-
1
r
A
N
+
1
r
B
N
Doc 14
0.7000, -6.0000, 10.0000, 0.7000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Vertical_electrical_sounding.html
a
0
2
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4
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Δ
2
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8
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3
a
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16
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2
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1
4
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1
8
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1
16
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⋯
.
Doc 15
0.7000, -31.0000, 10.0000, 0.7000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1_−_2_+_4_−_8_+_⋯.html
π
4
=
3
4
+
1
3
3
-
3
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1
5
3
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5
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1
7
3
-
7
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⋯
Doc 16
0.6889, -6.0000, 9.0000, 1.3021
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Kerala_school_of_astronomy_and_mathematics.html
Doc 17
0.6889, -6.0000, 9.0000, 1.3021
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Indian_mathematics.html
∑
k
=
1
n
-
1
1
p
k
=
1
r
-
1
p
n
=
p
n
-
r
r
p
n
=
1
p
r
,
Doc 18
0.6889, -15.0000, 10.0000, 0.6889
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Hölder's_inequality.html
1
-
1
2
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1
3
-
1
4
+
1
5
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⋯
=
ln
2.
Doc 19
0.6681, -8.0000, 10.0000, 1.3362
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 20
0.6681, -8.0000, 8.0000, 0.6681
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Euler_product.html
1
-
1
3
+
1
5
-
1
7
+
1
9
-
⋯
=
π
4
,
Doc 21
0.6681, -10.0000, 10.0000, 0.6681
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 22
0.6681, -10.0000, 10.0000, 0.6681
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Leibniz_formula_for_π.html
∑
n
=
1
∞
(
-
1
)
n
+
1
n
=
1
-
1
2
+
1
3
-
1
4
+
1
5
-
⋯
Doc 19
0.6681, -8.0000, 10.0000, 1.3362
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_series_(mathematics).html
Doc 23
0.6681, -19.0000, 10.0000, 0.6681
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
1
I
A
2
+
1
I
C
2
=
1
I
B
2
+
1
I
D
2
=
1
r
2
Doc 26
0.6522, -4.0000, 10.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Bicentric_quadrilateral.html
1
50
+
1
30
+
1
150
+
1
400
=
1
16
Doc 24
0.6522, -4.0000, 10.0000, 10.9565
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 24
0.6522, -4.0000, 10.0000, 10.9565
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 24
0.6522, -4.0000, 10.0000, 10.9565
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 24
0.6522, -4.0000, 10.0000, 10.9565
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1
τ
C
=
1
τ
U
+
1
τ
M
+
1
τ
B
+
1
τ
p
h
-
e
Doc 25
0.6522, -4.0000, 10.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Phonon_scattering.html
2
n
=
1
n
+
1
2
n
+
1
3
n
+
1
6
n
Doc 28
0.6522, -4.0000, 9.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Rhind_Mathematical_Papyrus_2::n_table.html
1
2
+
1
3
+
1
7
+
1
43
=
1805
1806
Doc 27
0.6522, -4.0000, 9.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Greedy_algorithm_for_Egyptian_fractions.html
26
97
=
1
4
+
1
97
+
1
194
+
1
388
Doc 29
0.6522, -4.0000, 9.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Ancient_Egyptian_multiplication.html
1
k
+
1
k
=
1
k
+
1
k
+
1
+
1
k
(
k
+
1
)
.
Doc 30
0.6522, -5.0000, 10.0000, 1.3043
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Egyptian_fraction.html
1
u
+
1
v
=
1
u
′
cos
θ
+
1
v
′
cos
θ
=
1
f
.
Doc 33
0.6522, -5.0000, 10.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Scheimpflug_principle.html
1
I
A
2
+
1
I
C
2
=
1
I
B
2
+
1
I
D
2
=
1
r
2
.
Doc 32
0.6522, -5.0000, 10.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Optic_equation.html
1
2
⋅
1
2
⋅
1
2
⋅
1
2
=
1
16
.
Doc 31
0.6522, -5.0000, 10.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Genetic_drift.html
1
r
1
2
+
1
r
2
2
+
1
r
3
2
+
1
r
4
2
≤
2
r
2
,
Doc 34
0.6522, -5.0000, 9.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Tetrahedron.html
8
11
=
1
2
+
1
22
+
1
6
+
1
66
.
Doc 30
0.6522, -5.0000, 10.0000, 1.3043
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Egyptian_fraction.html
1
2
=
1
3
+
1
9
+
1
27
+
1
81
+
⋯
Doc 1
1.0000, -8.0000, 14.0000, 1.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
1
w
=
1
a
+
1
b
+
1
c
+
1
d
(
=
0.0703
)
Doc 35
0.6522, -7.0000, 10.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Linkage_disequilibrium.html
1
r
1
+
1
r
4
=
1
r
2
+
1
r
5
=
1
r
3
+
1
r
6
.
Doc 36
0.6522, -10.0000, 10.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Soddy's_hexlet.html
13
20
=
10
20
+
2
20
+
1
20
=
1
2
+
1
10
+
1
20
.
Doc 37
0.6522, -13.0000, 9.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Practical_number.html
5
1
4
+
1
36
+
1
45
+
1
50
+
1
75
=
5
1
3
=
15.
Doc 38
0.6522, -14.0000, 10.0000, 0.6522
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Mean.html
254
147.333
+
199
147.333
+
225
147.333
-
253
150
-
110
150
-
103
150
.
Doc 39
0.6456, -11.0000, 8.0000, 1.1275
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Net_run_rate.html
π
4
=
1
-
1
3
+
1
5
-
1
7
+
…
Doc 16
0.6889, -6.0000, 9.0000, 1.3021
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
+
⋯
Doc 17
0.6889, -6.0000, 9.0000, 1.3021
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Indian_mathematics.html
U
S
.
Y
K
=
1
10
×
1
10
×
1
2
=
1
2
Doc 40
0.5957, -8.0000, 9.0000, 0.5957
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/James_Meade.html
n
=
E
ℏ
⋅
ω
-
1
2
=
m
ω
A
2
2
ℏ
-
1
2
Doc 41
0.5911, -8.0000, 8.0000, 0.5911
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Correspondence_principle.html
1
q
2
=
-
q
1
f
+
1
q
1
=
1
q
1
-
1
f
Doc 42
0.5581, -9.0000, 8.0000, 0.5581
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Ray_transfer_matrix_analysis.html
d
n
2
d
t
=
n
3
τ
32
+
n
1
τ
12
-
n
2
τ
21
-
n
2
τ
23
Doc 43
0.5581, -13.0000, 7.0000, 1.1163
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Quantum_cascade_laser.html
d
n
1
d
t
=
n
2
τ
21
+
n
3
τ
31
-
n
1
τ
13
-
n
1
τ
12
-
I
out
Doc 43
0.5581, -13.0000, 7.0000, 1.1163
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Quantum_cascade_laser.html
1
-
1
2
+
1
3
-
1
4
+
⋯
Doc 3
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Doc 46
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Doc 4
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Doc 24
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Doc 24
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Doc 24
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Doc 24
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Doc 24
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Doc 24
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Doc 24
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Doc 24
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Doc 24
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Doc 24
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Doc 24
0.6522, -4.0000, 10.0000, 10.9565
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Doc 24
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Doc 24
0.6522, -4.0000, 10.0000, 10.9565
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Doc 24
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Doc 24
0.6522, -4.0000, 10.0000, 10.9565
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 24
0.6522, -4.0000, 10.0000, 10.9565
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Doc 45
0.5217, -3.0000, 8.0000, 1.5652
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h
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Doc 44
0.5217, -3.0000, 8.0000, 1.5652
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Orthodiagonal_quadrilateral.html
Doc 45
0.5217, -3.0000, 8.0000, 1.5652
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Doc 45
0.5217, -3.0000, 8.0000, 1.5652
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h
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Doc 44
0.5217, -3.0000, 8.0000, 1.5652
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Doc 44
0.5217, -3.0000, 8.0000, 1.5652
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r
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Doc 47
0.5217, -3.0000, 8.0000, 0.5217
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R
a
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c
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Doc 48
0.5217, -4.0000, 8.0000, 2.0870
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Tangential_quadrilateral.html
1
h
1
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1
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Doc 48
0.5217, -4.0000, 8.0000, 2.0870
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1
r
1
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1
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Doc 48
0.5217, -4.0000, 8.0000, 2.0870
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1
r
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1
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Doc 48
0.5217, -4.0000, 8.0000, 2.0870
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1
r
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Doc 49
0.5217, -4.0000, 8.0000, 0.5217
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1
T
1
2
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1
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Doc 57
0.5217, -5.0000, 8.0000, 0.5217
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1
s
0
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Doc 53
0.5217, -5.0000, 8.0000, 0.5217
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Large_set_(combinatorics).html
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Y
T
S
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Y
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…
Doc 52
0.5217, -5.0000, 8.0000, 1.0435
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Z
T
P
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…
Doc 52
0.5217, -5.0000, 8.0000, 1.0435
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Doc 56
0.5217, -5.0000, 8.0000, 0.5217
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C
total
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Doc 50
0.5217, -5.0000, 8.0000, 2.0870
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Doc 50
0.5217, -5.0000, 8.0000, 2.0870
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Doc 55
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Doc 50
0.5217, -5.0000, 8.0000, 2.0870
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Doc 50
0.5217, -5.0000, 8.0000, 2.0870
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Doc 54
0.5217, -5.0000, 8.0000, 0.5217
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Electrical_impedance.html
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μ
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Doc 51
0.5217, -5.0000, 8.0000, 1.0435
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τ
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Doc 51
0.5217, -5.0000, 8.0000, 1.0435
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R
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Doc 58
0.5217, -6.0000, 8.0000, 0.5217
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N
x
∂
e
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X
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X
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X
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Q
∂
Q
∂
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e
Doc 59
0.5029, -18.0000, 7.0000, 0.5029
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2
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Doc 61
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P
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Doc 62
0.4819, -1.0000, 7.0000, 0.4819
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Δ
T
=
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Doc 60
0.4819, -1.0000, 7.0000, 0.4819
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p
*
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Doc 63
0.4819, -2.0000, 7.0000, 0.4819
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1
s
i
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Doc 64
0.4819, -2.0000, 7.0000, 0.4819
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254
97.333
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199
97.333
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253
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Doc 39
0.6456, -11.0000, 8.0000, 1.1275
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N
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1
N
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N
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×
1
N
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=
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Doc 65
0.4814, -13.0000, 7.0000, 0.4814
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ζ
(
3
)
3
-
π
2
γ
12
-
γ
3
6
Doc 66
0.4586, -8.0000, 6.0000, 0.4586
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k
2
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.
Doc 67
0.4473, -8.0000, 6.0000, 0.4473
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