tangent
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Search
Returned 100 matches (100 formulae, 53 docs)
Lookup 5.870 ms, Re-ranking 720.054 ms
Found 88932 tuple postings, 44940 formulae, 10804 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
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Doc 1
1.0000, 0.0000, 19.0000, 1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Backhouse's_constant.html
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Doc 2
1.0000, 0.0000, 16.0000, 2.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Square_root_of_2.html
2
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1
4
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1
4
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1
4
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1
4
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Doc 3
1.0000, 0.0000, 15.0000, 2.7295
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Square_root_of_5.html
1
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1
1
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1
1
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1
1
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1
1
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Doc 4
1.0000, 0.0000, 15.0000, 2.5672
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Golden_ratio.html
x
=
1
+
1
1
+
1
1
+
1
1
+
1
1
+
⋱
Doc 5
1.0000, -2.0000, 15.0000, 5.6061
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Generalized_continued_fraction.html
1
3
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1
1
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1
1
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1
3
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1
9
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Doc 6
1.0000, -2.0000, 14.0000, 1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Bernstein's_constant.html
1
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1
1
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1
1
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1
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1
1
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1
4
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Doc 7
1.0000, -4.0000, 17.0000, 1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Lieb's_square_ice_constant.html
1
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1
1
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1
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Doc 8
1.0000, -4.0000, 16.0000, 1.4231
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Square_root_of_3.html
2
=
1
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1
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1
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⋱
.
Doc 2
1.0000, 0.0000, 16.0000, 2.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Square_root_of_2.html
1
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1
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Doc 9
1.0000, -4.0000, 15.0000, 1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Transcendental_number.html
e
=
2
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1
1
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1
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1
1
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1
1
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1
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Doc 10
1.0000, -6.0000, 17.0000, 6.2816
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Gauss's_continued_fraction.html
π
=
3
+
1
2
6
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3
2
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5
2
6
+
7
2
6
+
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Doc 11
1.0000, -6.0000, 11.0000, 3.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
11
=
3
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1
3
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1
6
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1
3
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1
6
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1
3
+
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Doc 12
1.0000, -7.0000, 14.0000, 1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Square_root.html
2
=
1
+
1
2
+
1
2
+
1
2
+
1
2
+
1
2
+
⋱
.
Doc 13
1.0000, -8.0000, 15.0000, 1.9459
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Pell_number.html
π
=
4
1
+
1
2
3
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2
2
5
+
3
2
7
+
4
2
9
+
⋱
Doc 11
1.0000, -6.0000, 11.0000, 3.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
π
=
4
1
+
1
2
2
+
3
2
2
+
5
2
2
+
7
2
2
+
⋱
Doc 11
1.0000, -6.0000, 11.0000, 3.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
π
=
2
+
4
3
+
1
⋅
3
4
+
3
⋅
5
4
+
5
⋅
7
4
+
⋱
Doc 14
1.0000, -8.0000, 12.0000, 6.0839
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Continued_fraction.html
π
=
4
1
+
1
2
2
+
3
2
2
+
5
2
2
+
7
2
2
+
⋱
.
Doc 15
1.0000, -9.0000, 13.0000, 1.4653
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Euler's_continued_fraction_formula.html
x
=
1
+
1
2
+
1
2
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1
2
+
1
2
+
1
2
+
⋱
=
2
.
Doc 16
1.0000, -10.0000, 15.0000, 1.5670
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Solving_quadratic_equations_with_continued_fractions.html
4
π
=
1
+
1
2
2
+
3
2
2
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5
2
2
+
7
2
2
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9
2
2
+
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Doc 17
1.0000, -13.0000, 11.0000, 2.5670
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/William_Brouncker,_2nd_Viscount_Brouncker.html
π
=
3
+
1
7
+
1
15
+
1
1
+
1
292
+
1
1
+
1
1
+
1
1
+
⋱
Doc 18
1.0000, -14.0000, 15.0000, 1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Pi.html
e
=
1
+
2
1
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1
6
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1
10
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1
14
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1
18
+
1
22
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1
26
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.
Doc 19
1.0000, -15.0000, 14.0000, 1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/E_(mathematical_constant).html
π
4
=
1
1
+
1
2
2
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3
2
2
+
5
2
2
+
7
2
2
+
9
2
2
+
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Doc 17
1.0000, -13.0000, 11.0000, 2.5670
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/William_Brouncker,_2nd_Viscount_Brouncker.html
e
2
=
1
+
4
0
+
2
2
6
+
2
2
10
+
2
2
14
+
⋱
=
7
+
2
5
+
1
7
+
1
9
+
1
11
+
⋱
Doc 20
1.0000, -26.0000, 13.0000, 2.5670
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Exponential_function.html
e
3
=
1
+
6
-
1
+
3
2
6
+
3
2
10
+
3
2
14
+
⋱
=
13
+
54
7
+
9
14
+
9
18
+
9
22
+
⋱
Doc 20
1.0000, -26.0000, 13.0000, 2.5670
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Exponential_function.html
π
=
3
+
1
7
+
1
15
+
1
1
+
1
292
+
1
1
+
1
1
+
1
1
+
1
2
+
1
1
+
1
3
+
1
1
+
⋱
Doc 14
1.0000, -8.0000, 12.0000, 6.0839
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Continued_fraction.html
e
=
2
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1
1
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2
5
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1
10
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14
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18
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⋱
=
1
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2
1
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1
6
+
1
10
+
1
14
+
1
18
+
⋱
Doc 21
1.0000, -30.0000, 15.0000, 2.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/List_of_representations_of_e.html
e
=
2
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1
1
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1
2
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3
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4
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4
5
+
⋱
=
2
+
2
2
+
3
3
+
4
4
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5
5
+
6
6
+
⋱
Doc 21
1.0000, -30.0000, 15.0000, 2.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/List_of_representations_of_e.html
4
∫
0
∞
x
e
-
x
5
cosh
x
d
x
=
1
1
+
1
2
1
+
1
2
1
+
2
2
1
+
2
2
1
+
3
2
1
+
3
2
1
+
⋱
.
Doc 3
1.0000, 0.0000, 15.0000, 2.7295
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Square_root_of_5.html
π
=
2
+
2
1
+
1
1
/
2
+
1
1
/
3
+
1
1
/
4
+
⋱
=
2
+
2
1
+
1
⋅
2
1
+
2
⋅
3
1
+
3
⋅
4
1
+
⋱
Doc 14
1.0000, -8.0000, 12.0000, 6.0839
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Continued_fraction.html
log
2
=
log
(
1
+
1
)
=
1
1
+
1
2
+
1
3
+
2
2
+
2
5
+
3
2
+
⋱
=
2
3
-
1
2
9
-
2
2
15
-
3
2
21
-
⋱
Doc 5
1.0000, -2.0000, 15.0000, 5.6061
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Generalized_continued_fraction.html
ln
2
=
1
1
+
1
2
+
1
3
+
2
2
+
2
5
+
3
2
+
3
7
+
4
2
+
⋱
=
2
3
-
1
2
9
-
2
2
15
-
3
2
21
-
⋱
Doc 22
1.0000, -38.0000, 10.0000, 1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
1
1
+
1
0
+
1
8
+
1
4
+
1
1
+
1
0
+
1
/
⋯
Doc 23
0.9459, -9.0000, 14.0000, 1.8918
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
577
408
=
1
+
1
2
+
1
2
+
1
2
+
1
2
+
1
2
+
1
2
+
1
2
.
Doc 13
1.0000, -8.0000, 15.0000, 1.9459
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Pell_number.html
tanh
1
2
=
e
-
1
e
+
1
=
0
+
1
2
+
1
6
+
1
10
+
1
14
+
1
⋱
Doc 24
0.9459, -16.0000, 14.0000, 0.9459
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Singly_and_doubly_even.html
G
=
1
1
+
1
1
+
1
1
+
2
1
+
2
1
+
3
1
+
3
1
+
4
1
1
+
…
.
Doc 25
0.9459, -19.0000, 12.0000, 0.9459
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Gompertz_constant.html
I
1
(
2
)
I
0
(
2
)
=
∑
n
=
0
∞
n
n
!
n
!
∑
n
=
0
∞
1
n
!
n
!
=
1
1
+
1
2
+
1
3
+
1
4
+
1
5
+
1
6
+
1
/
⋯
Doc 23
0.9459, -9.0000, 14.0000, 1.8918
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
+
⋱
Doc 26
0.8918, -5.0000, 11.0000, 2.5672
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Approximations_of_π.html
π
4
=
1
1
+
1
2
2
+
3
2
2
+
5
2
2
+
⋱
=
1
-
1
3
+
1
5
-
1
7
+
-
…
Doc 10
1.0000, -6.0000, 17.0000, 6.2816
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Gauss's_continued_fraction.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 5
1.0000, -2.0000, 15.0000, 5.6061
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Generalized_continued_fraction.html
π
=
4
1
+
1
2
2
+
3
2
2
+
5
2
2
+
⋱
=
∑
n
=
0
∞
4
(
-
1
)
n
2
n
+
1
=
4
1
-
4
3
+
4
5
-
4
7
+
-
⋯
Doc 5
1.0000, -2.0000, 15.0000, 5.6061
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Generalized_continued_fraction.html
π
=
4
∑
n
=
0
∞
(
-
1
)
n
2
n
+
1
=
4
(
1
1
-
1
3
+
1
5
-
1
7
+
-
⋯
)
=
4
1
+
1
2
2
+
3
2
2
+
5
2
2
+
⋱
Doc 26
0.8918, -5.0000, 11.0000, 2.5672
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Approximations_of_π.html
1
+
1
4
+
1
1
+
1
18
+
1
⋱
Doc 28
0.8377, -1.0000, 13.0000, 0.8377
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Apéry's_constant.html
2
+
1
2
+
1
2
+
1
2
+
1
⋱
Doc 27
0.8377, -1.0000, 13.0000, 1.6213
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Silver_ratio.html
e
z
=
1
+
z
1
+
-
z
2
+
z
3
+
-
2
z
4
+
2
z
5
+
⋱
Doc 10
1.0000, -6.0000, 17.0000, 6.2816
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Gauss's_continued_fraction.html
e
z
=
1
1
+
-
z
1
+
z
2
+
-
z
3
+
2
z
4
+
-
2
z
5
+
⋱
Doc 10
1.0000, -6.0000, 17.0000, 6.2816
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Gauss's_continued_fraction.html
(
1
-
z
)
-
b
=
1
1
+
-
b
z
1
+
(
b
-
1
)
z
2
+
-
(
b
+
1
)
z
3
+
2
(
b
-
2
)
z
4
+
⋱
Doc 10
1.0000, -6.0000, 17.0000, 6.2816
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Gauss's_continued_fraction.html
Γ
(
s
,
z
)
=
z
s
e
-
z
z
+
1
-
s
1
+
1
z
+
2
-
s
1
+
2
z
+
3
-
s
1
+
⋱
Doc 29
0.8322, -24.0000, 12.0000, 0.8322
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Incomplete_gamma_function.html
φ
=
1
+
1
1
+
1
1
+
1
1
+
⋱
Doc 30
0.7836, -2.0000, 11.0000, 0.7836
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Fibonacci_number.html
δ
S
=
2
+
1
2
+
1
2
+
1
2
+
⋱
.
Doc 27
0.8377, -1.0000, 13.0000, 1.6213
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Silver_ratio.html
π
=
3
+
1
2
6
+
3
2
6
+
5
2
6
+
⋱
Doc 26
0.8918, -5.0000, 11.0000, 2.5672
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Approximations_of_π.html
x
=
1
+
z
1
+
z
1
+
z
1
+
z
1
+
⋱
Doc 5
1.0000, -2.0000, 15.0000, 5.6061
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Generalized_continued_fraction.html
φ
=
[
1
;
1
,
1
,
1
,
…
]
=
1
+
1
1
+
1
1
+
1
1
+
⋱
Doc 4
1.0000, 0.0000, 15.0000, 2.5672
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Golden_ratio.html
φ
-
1
=
[
0
;
1
,
1
,
1
,
…
]
=
0
+
1
1
+
1
1
+
1
1
+
⋱
Doc 4
1.0000, 0.0000, 15.0000, 2.5672
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Golden_ratio.html
arctan
z
=
z
1
+
(
1
z
)
2
3
+
(
2
z
)
2
5
+
(
3
z
)
2
7
+
(
4
z
)
2
9
+
⋱
,
Doc 10
1.0000, -6.0000, 17.0000, 6.2816
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Gauss's_continued_fraction.html
x
=
1
1
+
a
2
1
+
a
3
1
+
a
4
1
+
⋱
Doc 31
0.7295, -8.0000, 10.0000, 3.3647
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Convergence_problem.html
f
(
z
)
=
1
1
+
c
2
z
1
+
c
3
z
1
+
c
4
z
1
+
⋱
Doc 31
0.7295, -8.0000, 10.0000, 3.3647
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Convergence_problem.html
f
1
f
0
=
1
1
+
k
1
z
1
+
k
2
z
1
+
k
3
z
1
+
⋱
Doc 10
1.0000, -6.0000, 17.0000, 6.2816
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Gauss's_continued_fraction.html
1
1
+
e
-
2
π
1
+
e
-
4
π
1
+
e
-
6
π
1
+
⋱
=
(
5
+
5
2
-
5
+
1
2
)
e
2
π
/
5
=
e
2
π
/
5
(
φ
5
-
φ
)
.
Doc 3
1.0000, 0.0000, 15.0000, 2.7295
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Square_root_of_5.html
L
(
x
)
=
x
3
+
x
2
5
+
x
2
7
+
x
2
9
+
…
Doc 32
0.6753, -11.0000, 9.0000, 0.6753
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Brillouin_and_Langevin_functions.html
23
16
=
1
+
1
2
+
1
3
+
1
2
=
[
1
;
2
,
3
,
2
]
,
Doc 33
0.6753, -14.0000, 11.0000, 1.6728
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Stern–Brocot_tree.html
tan
(
x
)
=
x
1
+
-
x
2
3
+
-
x
2
5
+
-
x
2
7
+
⋱
Doc 5
1.0000, -2.0000, 15.0000, 5.6061
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Generalized_continued_fraction.html
y
=
1
+
z
1
+
z
1
+
z
1
+
⋱
Doc 31
0.7295, -8.0000, 10.0000, 3.3647
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Convergence_problem.html
f
(
z
)
=
1
+
z
1
+
z
1
+
z
1
+
z
⋱
.
Doc 34
0.6212, -10.0000, 9.0000, 0.6212
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Complex_plane.html
x
=
1
+
x
-
1
2
+
x
-
1
2
+
x
-
1
2
+
⋱
Doc 14
1.0000, -8.0000, 12.0000, 6.0839
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Continued_fraction.html
1
+
q
1
+
q
2
1
+
q
3
1
+
⋯
=
G
(
q
)
H
(
q
)
.
Doc 35
0.6212, -14.0000, 7.0000, 0.6212
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Rogers–Ramanujan_identities.html
c
0
+
K
n
=
1
∞
1
c
n
=
c
0
+
1
c
1
+
1
c
2
+
1
c
3
+
1
c
4
+
⋱
Doc 36
0.5957, -23.0000, 14.0000, 0.5957
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Infinite_expression_(mathematics).html
n
+
1
n
+
1
n
+
1
n
+
1
n
+
⋱
=
[
n
;
n
,
n
,
n
,
n
,
…
]
=
1
2
(
n
+
n
2
+
4
)
Doc 37
0.5957, -30.0000, 14.0000, 0.5957
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Metallic_mean.html
x
=
[
a
0
;
a
1
,
a
2
,
…
]
=
a
0
+
1
a
1
+
1
a
2
+
1
a
3
+
1
a
4
+
⋱
=
a
0
+
K
i
=
1
∞
1
a
i
,
Doc 38
0.5957, -38.0000, 14.0000, 0.5957
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Restricted_partial_quotients.html
1
15
+
1
1
+
1
102
Doc 14
1.0000, -8.0000, 12.0000, 6.0839
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Continued_fraction.html
e
z
=
1
+
2
z
2
-
z
+
z
2
6
+
z
2
10
+
z
2
14
+
⋱
Doc 20
1.0000, -26.0000, 13.0000, 2.5670
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Exponential_function.html
1
1
+
1
2
2
+
3
2
2
=
13
15
=
1
-
1
3
+
1
5
.
Doc 17
1.0000, -13.0000, 11.0000, 2.5670
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/William_Brouncker,_2nd_Viscount_Brouncker.html
x
=
1
+
1
1
+
(
1
+
1
1
+
x
)
=
1
+
1
2
+
1
1
+
x
.
Doc 16
1.0000, -10.0000, 15.0000, 1.5670
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Solving_quadratic_equations_with_continued_fractions.html
q
=
a
0
+
1
a
1
+
1
a
2
+
1
a
3
+
1
⋱
+
1
a
k
=
[
a
0
;
a
1
,
a
2
,
…
,
a
k
]
Doc 33
0.6753, -14.0000, 11.0000, 1.6728
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Stern–Brocot_tree.html
a
0
+
1
a
1
+
1
a
2
+
1
⋱
+
1
a
n
,
Doc 39
0.5217, -10.0000, 12.0000, 0.5217
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Rational_number.html
x
=
a
0
+
1
a
1
+
1
a
2
+
1
a
3
+
1
⋱
Doc 40
0.5217, -11.0000, 12.0000, 0.5217
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Khinchin's_constant.html
Doc 41
0.5217, -11.0000, 12.0000, 0.5217
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Borel_set.html
x
=
[
a
0
;
a
1
,
a
2
,
a
3
,
…
]
=
a
0
+
1
a
1
+
1
a
2
+
1
a
3
+
1
⋱
,
Doc 42
0.5217, -27.0000, 12.0000, 0.5217
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Complete_quotient.html
a
b
=
q
0
+
1
q
1
+
1
q
2
+
1
⋱
+
1
q
N
=
[
q
0
;
q
1
,
q
2
,
…
,
q
N
]
.
Doc 43
0.5217, -29.0000, 12.0000, 0.5217
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Euclidean_algorithm.html
x
=
z
-
1
1
+
z
-
2
1
+
z
-
2
1
+
⋱
Doc 31
0.7295, -8.0000, 10.0000, 3.3647
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Convergence_problem.html
f
(
z
)
=
a
1
z
1
+
a
2
z
1
+
a
3
z
1
+
a
4
z
⋱
Doc 44
0.5128, -17.0000, 7.0000, 0.5128
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Chain_sequence.html
x
=
a
0
+
1
a
1
+
1
a
2
+
1
a
3
+
⋱
.
Doc 45
0.4653, -11.0000, 11.0000, 0.4653
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Hermite's_problem.html
S
=
a
0
+
1
a
1
+
1
a
2
+
1
a
3
+
⋱
Doc 46
0.4653, -11.0000, 11.0000, 0.4653
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Methods_of_computing_square_roots.html
r
=
a
0
+
1
a
1
+
1
a
2
+
1
a
3
+
⋯
,
Doc 47
0.4653, -11.0000, 10.0000, 0.4653
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Mathematical_constant.html
x
=
1
1
+
a
2
b
2
+
a
3
b
3
+
a
4
b
4
+
⋱
Doc 15
1.0000, -9.0000, 13.0000, 1.4653
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Euler's_continued_fraction_formula.html
-
3
+
1
2
+
1
18
Doc 14
1.0000, -8.0000, 12.0000, 6.0839
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Continued_fraction.html
[
1
;
2
,
3
,
1
]
=
[
1
;
2
,
4
]
=
1
+
1
2
+
1
4
=
13
9
.
Doc 33
0.6753, -14.0000, 11.0000, 1.6728
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Stern–Brocot_tree.html
[
2
;
-
4
,
-
4
,
-
4
,
…
]
=
2
-
1
4
-
1
4
-
1
4
-
⋱
Doc 8
1.0000, -4.0000, 16.0000, 1.4231
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Square_root_of_3.html
x
=
K
1
∞
1
z
=
1
z
+
1
z
+
1
z
+
⋱
Doc 31
0.7295, -8.0000, 10.0000, 3.3647
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Convergence_problem.html
a
+
1
b
+
1
c
+
1
⋱
Doc 48
0.3913, -4.0000, 9.0000, 0.3913
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Budan's_theorem.html
2
c
+
2
d
+
2
4
=
a
Doc 49
0.3913, -4.0000, 6.0000, 0.3913
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Help:Displaying_a_formula.html
a
1
+
1
a
2
+
1
a
3
+
1
⋱
Doc 50
0.3913, -7.0000, 9.0000, 0.3913
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Vincent's_theorem.html
a
0
+
1
a
1
+
1
a
2
+
1
a
3
Doc 14
1.0000, -8.0000, 12.0000, 6.0839
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Continued_fraction.html
x
=
a
0
+
1
a
1
+
1
a
2
+
1
a
3
Doc 14
1.0000, -8.0000, 12.0000, 6.0839
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Continued_fraction.html
x
=
b
0
+
a
1
b
1
+
a
2
b
2
+
a
3
b
3
+
a
4
b
4
+
⋱
Doc 5
1.0000, -2.0000, 15.0000, 5.6061
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Generalized_continued_fraction.html
Doc 14
1.0000, -8.0000, 12.0000, 6.0839
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Continued_fraction.html
x
=
b
0
+
a
1
b
1
+
a
2
b
2
+
a
3
b
3
+
a
4
b
4
+
⋱
.
Doc 31
0.7295, -8.0000, 10.0000, 3.3647
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Convergence_problem.html
F
1
0
(
a
+
1
;
z
)
a
0
F
1
(
a
;
z
)
=
1
a
+
z
(
a
+
1
)
+
z
(
a
+
2
)
+
z
(
a
+
3
)
+
⋱
Doc 10
1.0000, -6.0000, 17.0000, 6.2816
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Gauss's_continued_fraction.html
p
(
z
)
=
a
0
z
+
a
1
z
+
a
2
z
+
a
3
z
+
⋱
Doc 51
0.3025, -16.0000, 9.0000, 0.3025
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Factorial.html
a
0
+
b
1
a
1
+
b
2
a
2
+
b
3
a
3
+
⋱
Doc 14
1.0000, -8.0000, 12.0000, 6.0839
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Continued_fraction.html
1
+
1
2
+
1
3
+
1
4
+
1
5
+
⋯
Doc 52
0.2410, -14.0000, 5.0000, 0.2410
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Logarithmic_growth.html
a
1
b
1
+
a
2
b
2
+
a
3
b
3
+
⋱
Doc 53
0.2295, -12.0000, 7.0000, 0.2295
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Śleszyński–Pringsheim_theorem.html