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Search
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 ]
2
3
-
1
2
=
4
6
-
3
6
=
1
6
Doc 1
0.6724, 1.0554
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Fraction_(mathematics).html
1
r
min
-
1
p
=
1
p
-
1
r
max
Doc 2
0.6280, 0.6280
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Kepler's_laws_of_planetary_motion.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 3
0.5889, 0.5889
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Biexciton.html
1
18
=
1
2
-
1
3
-
1
3
2
.
Doc 4
0.5748, 0.5748
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Partial_fraction_decomposition.html
∑
k
=
0
∞
1
16
k
(
4
8
k
+
1
-
2
8
k
+
4
-
1
8
k
+
5
-
1
8
k
+
6
)
=
π
Doc 5
0.5656, 0.5656
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
1
1
-
1
2
+
1
3
-
1
4
+
1
5
⋯
=
ln
(
2
)
Doc 6
0.5590, 0.9719
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
π
4
=
3
4
+
1
3
3
-
3
-
1
5
3
-
5
+
1
7
3
-
7
-
⋯
Doc 7
0.5576, 1.0175
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Indian_mathematics.html
Doc 8
0.5576, 1.0175
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Kerala_school_of_astronomy_and_mathematics.html
x
-
1
-
1
2
-
1
4
-
1
5
-
1
6
-
1
9
-
⋯
=
1
Doc 9
0.5541, 0.9790
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
k
=
2
π
1
r
A
M
-
1
r
B
M
-
1
r
A
N
+
1
r
B
N
Doc 10
0.5125, 0.5125
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Vertical_electrical_sounding.html
1
I
A
2
+
1
I
C
2
=
1
I
B
2
+
1
I
D
2
=
1
r
2
Doc 11
0.5119, 0.5119
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Bicentric_quadrilateral.html
1
τ
C
=
1
τ
U
+
1
τ
M
+
1
τ
B
+
1
τ
p
h
-
e
Doc 12
0.5100, 0.5100
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Phonon_scattering.html
1
I
A
2
+
1
I
C
2
=
1
I
B
2
+
1
I
D
2
=
1
r
2
.
Doc 13
0.4974, 0.4974
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Optic_equation.html
1
k
+
1
k
=
1
k
+
1
k
+
1
+
1
k
(
k
+
1
)
.
Doc 14
0.4925, 0.9351
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 15
0.4852, 0.4852
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Scheimpflug_principle.html
2
n
=
1
n
+
1
2
n
+
1
3
n
+
1
6
n
Doc 16
0.4821, 0.4821
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Rhind_Mathematical_Papyrus_2::n_table.html
22
7
-
1
630
<
π
<
22
7
-
1
1260
,
Doc 17
0.4798, 0.4798
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Proof_that_22::7_exceeds_π.html
1
50
+
1
30
+
1
150
+
1
400
=
1
16
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 18
0.4713, 8.0127
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 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
ln
2
=
1
1
-
1
2
+
1
3
-
1
4
+
1
5
-
⋯
.
Doc 19
0.4689, 0.4689
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
1
r
1
2
+
1
r
2
2
+
1
r
3
2
+
1
r
4
2
≤
2
r
2
,
Doc 20
0.4680, 0.4680
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Tetrahedron.html
26
97
=
1
4
+
1
97
+
1
194
+
1
388
Doc 21
0.4655, 0.4655
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Ancient_Egyptian_multiplication.html
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
=
1
-
1
3
+
1
5
-
1
7
+
⋯
Doc 7
0.5576, 1.0175
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Indian_mathematics.html
1
-
1
2
-
1
4
+
1
8
-
1
16
+
⋯
=
1
3
.
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
2
⋅
1
2
⋅
1
2
⋅
1
2
=
1
16
.
Doc 23
0.4481, 0.4481
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Genetic_drift.html
∑
k
=
1
n
-
1
1
p
k
=
1
r
-
1
p
n
=
p
n
-
r
r
p
n
=
1
p
r
,
Doc 24
0.4445, 0.4445
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Hölder's_inequality.html
8
11
=
1
2
+
1
22
+
1
6
+
1
66
.
Doc 14
0.4925, 0.9351
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Egyptian_fraction.html
1
2
+
1
3
+
1
7
+
1
43
=
1805
1806
Doc 25
0.4425, 0.4425
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Greedy_algorithm_for_Egyptian_fractions.html
254
147.333
+
199
147.333
+
225
147.333
-
253
150
-
110
150
-
103
150
.
Doc 26
0.4425, 0.8344
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Net_run_rate.html
∑
k
=
1
∞
(
-
1
)
k
s
k
-
1
=
1
1
-
1
2
+
1
6
-
1
42
+
1
1806
±
⋯
Doc 27
0.4414, 2.7191
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
d
n
2
d
t
=
n
3
τ
32
+
n
1
τ
12
-
n
2
τ
21
-
n
2
τ
23
Doc 28
0.4390, 0.8364
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Quantum_cascade_laser.html
∏
p
(
1
-
3
p
3
+
2
p
4
+
1
p
5
-
1
p
6
)
=
0.678234...
Doc 29
0.4355, 0.4355
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Euler_product.html
1
2
=
1
3
+
1
9
+
1
27
+
1
81
+
⋯
Doc 9
0.5541, 0.9790
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Goldbach–Euler_theorem.html
1
-
1
2
+
1
3
-
1
4
+
1
5
-
⋯
=
ln
2.
Doc 30
0.4229, 0.7645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_series_(mathematics).html
∑
n
=
0
∞
(
-
1
)
n
n
!
=
1
0
!
-
1
1
!
+
1
2
!
-
1
3
!
+
1
4
!
-
1
5
!
+
⋯
Doc 27
0.4414, 2.7191
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
3
.
Doc 6
0.5590, 0.9719
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
n
=
E
ℏ
⋅
ω
-
1
2
=
m
ω
A
2
2
ℏ
-
1
2
Doc 31
0.4112, 0.4112
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Correspondence_principle.html
1
h
1
2
+
1
h
3
2
=
1
h
2
2
+
1
h
4
2
Doc 32
0.4056, 1.2090
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Orthodiagonal_quadrilateral.html
Doc 32
0.4056, 1.2090
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Orthodiagonal_quadrilateral.html
∑
n
=
1
∞
(
-
1
)
n
+
1
n
!
=
1
1
!
-
1
2
!
+
1
3
!
-
1
4
!
+
1
5
!
-
1
6
!
+
⋯
Doc 27
0.4414, 2.7191
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
N
-
1
N
×
N
-
2
N
-
1
×
N
-
3
N
-
2
×
1
N
-
3
=
1
N
Doc 33
0.4038, 0.4038
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Drawing_straws.html
1
-
1
2
+
1
3
-
1
4
+
⋯
Doc 34
0.4026, 0.7606
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Riemann_series_theorem.html
1
w
=
1
a
+
1
b
+
1
c
+
1
d
(
=
0.0703
)
Doc 35
0.4020, 0.4020
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Linkage_disequilibrium.html
1
B
𝑒𝑓𝑓
=
1
B
l
+
1
B
e
q
+
1
B
g
Doc 36
0.4014, 0.4014
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Water_hammer.html
1
s
i
-
1
-
1
s
i
+
1
-
1
=
1
s
i
,
Doc 37
0.4011, 0.4011
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sylvester's_sequence.html
3
3
4
(
1
-
1
2
2
+
1
4
2
-
1
5
2
+
1
7
2
-
1
8
2
+
1
10
2
±
⋯
)
Doc 27
0.4414, 2.7191
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
1
h
1
+
1
h
4
=
1
h
2
+
1
h
3
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
3
=
1
h
2
+
1
h
4
Doc 32
0.4056, 1.2090
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Orthodiagonal_quadrilateral.html
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
2
=
1
h
3
+
1
h
4
Doc 38
0.3978, 1.1935
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Ex-tangential_quadrilateral.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 28
0.4390, 0.8364
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Quantum_cascade_laser.html
1
2
-
1
4
=
1
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
r
=
1
h
a
+
1
h
b
+
1
h
c
Doc 40
0.3946, 0.3946
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Triangle.html
1
r
1
+
1
r
4
=
1
r
2
+
1
r
5
=
1
r
3
+
1
r
6
.
Doc 41
0.3930, 0.3930
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Soddy's_hexlet.html
254
97.333
+
199
97.333
-
253
100
-
110
100
.
Doc 26
0.4425, 0.8344
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Net_run_rate.html
1
R
a
+
1
R
c
=
1
R
b
+
1
R
d
.
Doc 42
0.3848, 1.5391
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Tangential_quadrilateral.html
1
h
1
+
1
h
3
=
1
h
2
+
1
h
4
.
Doc 42
0.3848, 1.5391
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Tangential_quadrilateral.html
1
r
1
+
1
r
3
=
1
r
2
+
1
r
4
.
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
.
Doc 42
0.3848, 1.5391
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Tangential_quadrilateral.html
1
3
+
1
4
+
1
6
+
1
68
Doc 1
0.6724, 1.0554
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Fraction_(mathematics).html
1
22
+
1
33
+
1
66
=
1
11
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1
28
+
1
49
+
1
196
=
1
13
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1
30
+
1
45
+
1
90
=
1
15
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1
6
+
1
6
+
1
6
=
1
2
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1
7
+
1
14
+
1
28
=
1
4
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1
25
+
1
50
+
1
150
=
1
6
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1
14
+
1
21
+
1
42
=
1
7
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1
18
+
1
27
+
1
54
=
1
9
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
Doc 18
0.4713, 8.0127
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Egyptian_Mathematical_Leather_Roll.html
1
q
2
=
-
q
1
f
+
1
q
1
=
1
q
1
-
1
f
Doc 43
0.3823, 0.3823
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Ray_transfer_matrix_analysis.html
1
T
1
2
=
1
t
1
+
1
t
2
+
1
t
3
+
⋯
Doc 44
0.3814, 0.3814
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Half-life.html
1
r
=
1
h
a
+
1
h
b
+
1
h
c
.
Doc 45
0.3811, 0.3811
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Altitude_(triangle).html
1
-
1
3
+
1
5
-
1
7
+
1
9
-
⋯
=
π
4
,
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
Y
T
S
=
1
Y
1
+
1
Y
2
+
1
Y
3
+
…
Doc 48
0.3764, 0.7529
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Smith_chart.html
1
Z
T
P
=
1
Z
1
+
1
Z
2
+
1
Z
3
+
…
Doc 48
0.3764, 0.7529
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Smith_chart.html
5
1
4
+
1
36
+
1
45
+
1
50
+
1
75
=
5
1
3
=
15.
Doc 49
0.3761, 0.3761
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Mean.html
-
ζ
(
3
)
3
-
π
2
γ
12
-
γ
3
6
Doc 50
0.3709, 0.3709
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Factorial.html
1
s
0
+
1
s
1
+
1
s
2
+
1
s
3
+
⋯
Doc 51
0.3709, 0.3709
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Large_set_(combinatorics).html
1
P
s
y
n
=
1
P
1
-
1
P
2
Doc 52
0.3700, 0.3700
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Orbital_period.html
1
μ
=
1
μ
impurities
+
1
μ
lattice
+
1
μ
defects
+
⋯
Doc 53
0.3668, 0.7335
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Electron_mobility.html
1
τ
=
1
τ
impurities
+
1
τ
lattice
+
1
τ
defects
+
⋯
Doc 53
0.3668, 0.7335
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Electron_mobility.html
1
Δ
T
=
1
T
1
-
1
T
2
Doc 54
0.3659, 0.3659
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pendulum.html
1
C
eq
=
1
C
1
+
1
C
2
+
⋯
+
1
C
n
Doc 58
0.3611, 0.3611
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Capacitor.html
1
C
total
=
1
C
1
+
1
C
2
+
⋯
+
1
C
n
Doc 55
0.3611, 1.4442
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Series_and_parallel_circuits.html
1
G
total
=
1
G
1
+
1
G
2
+
⋯
+
1
G
n
Doc 55
0.3611, 1.4442
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Series_and_parallel_circuits.html
1
L
eq
=
1
L
1
+
1
L
2
+
⋯
+
1
L
n
Doc 57
0.3611, 0.3611
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Inductor.html
1
L
total
=
1
L
1
+
1
L
2
+
⋯
+
1
L
n
Doc 55
0.3611, 1.4442
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Series_and_parallel_circuits.html
1
R
total
=
1
R
1
+
1
R
2
+
⋯
+
1
R
n
Doc 55
0.3611, 1.4442
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Series_and_parallel_circuits.html
1
Z
eq
=
1
Z
1
+
1
Z
2
+
⋯
+
1
Z
n
Doc 56
0.3611, 0.3611
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Electrical_impedance.html
1
-
1
2
-
1
4
+
1
3
-
1
6
-
1
8
+
1
5
-
1
10
-
1
12
+
⋯
Doc 34
0.4026, 0.7606
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Riemann_series_theorem.html
π
4
=
∑
n
=
0
∞
(
-
1
)
n
2
n
+
1
=
1
1
-
1
3
+
1
5
-
1
7
+
1
9
-
⋯
Doc 27
0.4414, 2.7191
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
+
⋯
Doc 27
0.4414, 2.7191
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
1
R
T
=
1
R
1
+
1
R
2
+
1
R
3
+
…
.
Doc 59
0.3563, 0.3563
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Current_divider.html
1
p
*
=
1
p
-
1
n
.
Doc 60
0.3504, 0.3504
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sobolev_inequality.html
∑
n
=
1
∞
(
-
1
)
⌊
n
-
1
2
⌋
2
n
+
1
=
1
1
+
1
3
-
1
5
-
1
7
+
1
9
+
1
11
-
⋯
Doc 27
0.4414, 2.7191
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
k
2
m
=
k
m
-
k
m
+
k
m
-
⋯
.
Doc 61
0.3464, 0.3464
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/History_of_Grandi's_series.html
U
S
.
Y
K
=
1
10
×
1
10
×
1
2
=
1
2
Doc 62
0.3419, 0.3419
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/James_Meade.html
∑
n
=
1
∞
(
-
1
)
n
+
1
n
=
1
-
1
2
+
1
3
-
1
4
+
1
5
-
⋯
Doc 30
0.4229, 0.7645
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_series_(mathematics).html
Doc 63
0.3416, 0.3416
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
C
=
∑
(
-
1
)
i
s
i
-
1
=
1
1
-
1
2
+
1
6
-
1
42
+
1
1806
-
⋯
≈
0.64341054629.
Doc 64
0.3373, 0.3373
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Cahen's_constant.html
13
20
=
10
20
+
2
20
+
1
20
=
1
2
+
1
10
+
1
20
.
Doc 65
0.2924, 0.2924
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Practical_number.html
∂
N
x
∂
e
1
X
=
∂
X
∂
e
1
X
-
1
Q
∂
Q
∂
e
-
1
e
Doc 66
0.2654, 0.2654
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Marshall–Lerner_condition.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 67
0.1845, 0.1845
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/1_−_2_+_4_−_8_+_⋯.html