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Search
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 ]
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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
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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
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∞
(
(
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1
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arctan
1
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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
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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
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Doc 5
0.6723, -10.0000, 17.0000, 4.3284
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Convergent_series.html
π
=
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Doc 6
0.6723, -11.0000, 10.0000, 1.7328
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pi.html
∑
n
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1
∞
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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
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⋱
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34
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3145
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4551
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6601
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38341
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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
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∑
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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
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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
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∞
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n
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1
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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
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1
∞
(
-
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⌊
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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
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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
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Doc 6
0.6723, -11.0000, 10.0000, 1.7328
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pi.html
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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
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1
∞
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!
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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
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k
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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
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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
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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
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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
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1
5
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1
7
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1
9
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⋯
=
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
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9
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⋯
=
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
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16
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3
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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
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1
3
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1
4
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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
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1
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1
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1
5
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⋯
=
∑
n
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1
∞
(
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1
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n
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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
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⋯
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∑
n
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1
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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
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a
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2
a
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1
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⋯
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1
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a
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1
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1
2
b
+
2
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⋯
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
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3
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1
5
3
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5
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1
7
3
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7
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⋯
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
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1
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n
+
1
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1
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⋅
2
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5
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7
⋅
2
7
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⋯
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
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1
2
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1
4
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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
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1
3
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1
6
+
1
10
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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
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1
4
+
1
5
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⋯
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
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1
4
+
1
8
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1
16
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⋯
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1
/
2
1
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(
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1
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2
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1
3
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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
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n
2
n
+
1
)
3
=
1
1
3
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1
3
3
+
1
5
3
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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
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n
2
n
+
1
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5
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1
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5
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5
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1
5
5
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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
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1
16
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⋯
.
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
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2
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1
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1
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k
,
k
=
1
,
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,
…
.
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
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1
5
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1
7
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⋯
+
(
-
1
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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
∞
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=
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
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1807
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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
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1
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9
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⋯
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
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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
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1
9
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1
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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
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1
2
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1
9
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1
145
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37986
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⋯
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
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2
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11
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→
∞
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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
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1
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1
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1
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…
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
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3
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→
∞
.
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
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1
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1
9
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1
10
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1
11
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⋯
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
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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
-
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1
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=
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
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+
1
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1
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+
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±
1
n
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)
=
n
!
∑
k
=
0
n
(
-
1
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k
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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
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⋱
=
1
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1
3
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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
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1
4
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1
8
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1
16
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=
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
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1
150
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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
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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
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1
2
⋅
1
2
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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
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1
3
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1
7
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1
43
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⋯
=
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
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1
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1
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1
8
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1
16
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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
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O
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B
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B
E
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E
O
1
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E
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1
-
1
2
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13
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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
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1
7
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⋯
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
∞
(
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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
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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
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1
4
+
1
5
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⋯
=
∑
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
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1
4
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1
8
+
1
16
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⋯
=
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
∞
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1
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n
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1
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1
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2
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1
3
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⋯
.
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
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1
3
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1
4
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⋯
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
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2
+
1
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⋯
)
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
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1
2
2
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3
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2
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15
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1
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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
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1
6
)
-
1
8
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(
1
5
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1
10
)
-
1
12
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⋯
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
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1
4
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8
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⋯
+
1
2
n
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⋯
.
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
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1
4
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1
8
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1
16
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⋯
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
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1
3
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1
4
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1
5
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⋯
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
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+
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
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1
2
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3
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1
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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
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1
n
=
1
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1
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5
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⋯
.
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
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2
p
4
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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
!
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x
3
3
!
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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
-
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1
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2
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0
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⋯
=
1
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4
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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
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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
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1
∞
1
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1
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1
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1
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4
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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
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x
-
1
2
x
2
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1
3
x
3
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1
4
x
4
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⋯
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