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0.026838601
…
Search
Returned 32 matches (40 formulae, 24 docs)
Lookup 0.311 ms, Re-ranking 60.890 ms
Found 42 tuple postings, 40 formulae, 24 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
Doc 1
1.0000
0.0000
3.0000
4.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Prime_zeta_function.html
-
0.026838601
…
-
0.060607633
…
-
0.150757555
…
-
0.493091109
…
Doc 2
1.0000
-2.0000
2.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Quintic_function.html
x
=
-
1.84208
…
Doc 3
1.0000
-5.0000
2.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Nth_root.html
-
2
5
=
-
1.148698354
…
Doc 4
1.0000
-6.0000
2.0000
6.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Pell_number.html
1393
-
985
2
=
-
0.00035
…
1
-
1
2
=
-
0.41421
…
239
-
169
2
=
-
0.00209
…
41
-
29
2
=
-
0.01219
…
7
-
5
2
=
-
0.07106
…
8119
-
5741
2
=
-
0.00006
…
Doc 5
1.0000
-7.0000
2.0000
2.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Trigamma_function.html
z
1
=
-
0.4121345
…
+
i
0.5978119
…
z
2
=
-
1.4455692
…
+
i
0.6992608
…
Doc 6
1.0000
-7.0000
2.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Vienna_rectifier.html
ϕ
1
=
-
30
∘
…
+
30
∘
Doc 7
1.0000
-8.0000
2.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Srinivasa_Ramanujan.html
e
π
58
=
396
4
-
104.000000177
…
.
Doc 8
1.0000
-10.0000
2.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Spiral_of_Theodorus.html
lim
k
→
∞
c
2
(
k
)
=
-
2.157782996659
…
.
Doc 9
1.0000
-13.0000
2.0000
2.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Particular_values_of_Riemann_zeta_function.html
ζ
′
(
-
1
)
=
1
12
-
ln
A
≈
-
0.1654211437
…
ζ
′
(
0
)
=
-
1
2
ln
(
2
π
)
≈
-
0.918938533
…
Doc 10
1.0000
-14.0000
2.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Mathematical_coincidence.html
(
π
+
20
)
i
=
-
0.9999999992
…
-
i
⋅
0.000039
…
≈
-
1
Doc 11
1.0000
-20.0000
2.0000
4.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Stieltjes_constants.html
γ
1
(
1
2
)
=
-
2
γ
ln
2
-
ln
2
2
+
γ
1
=
-
1.353459680
…
γ
1
(
1
4
)
=
2
π
ln
Γ
(
1
4
)
-
3
π
2
ln
π
-
7
2
ln
2
2
-
(
3
γ
+
2
π
)
ln
2
-
γ
π
2
+
γ
1
=
-
5.518076350
…
γ
1
(
3
4
)
=
-
2
π
ln
Γ
(
1
4
)
+
3
π
2
ln
π
-
7
2
ln
2
2
-
(
3
γ
-
2
π
)
ln
2
+
γ
π
2
+
γ
1
=
-
0.3912989024
…
γ
1
(
1
3
)
=
-
3
γ
2
ln
3
-
3
4
ln
2
3
+
π
4
3
{
ln
3
-
8
ln
2
π
-
2
γ
+
12
ln
Γ
(
1
3
)
}
+
γ
1
=
-
3.259557515
…
γ
1
(
2
3
)
=
-
3
γ
2
ln
3
-
3
4
ln
2
3
-
π
4
3
{
ln
3
-
8
ln
2
π
-
2
γ
+
12
ln
Γ
(
1
3
)
}
+
γ
1
=
-
0.5989062842
…
γ
1
(
1
6
)
=
-
3
γ
2
ln
3
-
3
4
ln
2
3
-
ln
2
2
-
(
3
ln
3
+
2
γ
)
ln
2
+
3
π
3
2
ln
Γ
(
1
6
)
-
π
2
3
{
3
ln
3
+
11
ln
2
+
15
2
ln
π
+
3
γ
}
+
γ
1
=
-
10.74258252
…
γ
1
(
5
6
)
=
-
3
γ
2
ln
3
-
3
4
ln
2
3
-
ln
2
2
-
(
3
ln
3
+
2
γ
)
ln
2
-
3
π
3
2
ln
Γ
(
1
6
)
+
π
2
3
{
3
ln
3
+
11
ln
2
+
15
2
ln
π
+
3
γ
}
+
γ
1
=
-
0.2461690038
…
γ
1
(
1
5
)
=
γ
1
+
5
2
{
ζ
′′
(
0
,
1
5
)
+
ζ
′′
(
0
,
4
5
)
}
+
π
10
+
2
5
2
ln
Γ
(
1
5
)
+
π
10
-
2
5
2
ln
Γ
(
2
5
)
+
{
5
2
ln
2
-
5
2
ln
(
1
+
5
)
-
5
4
ln
5
-
π
25
+
10
5
10
}
⋅
γ
-
5
2
{
ln
2
+
ln
5
+
ln
π
+
π
25
-
10
5
10
}
⋅
ln
(
1
+
5
)
+
5
2
ln
2
2
+
5
(
1
-
5
)
8
ln
2
5
+
3
5
4
ln
2
⋅
ln
5
+
5
2
ln
2
⋅
ln
π
+
5
4
ln
5
⋅
ln
π
-
π
(
2
25
+
10
5
+
5
25
+
2
5
)
20
ln
2
-
π
(
4
25
+
10
5
-
5
5
+
2
5
)
40
ln
5
-
π
(
5
5
+
2
5
+
25
+
10
5
)
10
ln
π
=
-
8.030205511
…
γ
1
(
1
8
)
=
γ
1
+
2
{
ζ
′′
(
0
,
1
8
)
+
ζ
′′
(
0
,
7
8
)
}
+
2
π
2
ln
Γ
(
1
8
)
-
π
2
(
1
-
2
)
ln
Γ
(
1
4
)
-
{
1
+
2
2
π
+
4
ln
2
+
2
ln
(
1
+
2
)
}
⋅
γ
-
1
2
(
π
+
8
ln
2
+
2
ln
π
)
⋅
ln
(
1
+
2
)
-
7
(
4
-
2
)
4
ln
2
2
+
1
2
ln
2
⋅
ln
π
-
π
(
10
+
11
2
)
4
ln
2
-
π
(
3
+
2
2
)
2
ln
π
=
-
16.64171976
…
γ
1
(
1
12
)
=
γ
1
+
3
{
ζ
′′
(
0
,
1
12
)
+
ζ
′′
(
0
,
11
12
)
}
+
4
π
ln
Γ
(
1
4
)
+
3
π
3
ln
Γ
(
1
3
)
-
{
2
+
3
2
π
+
3
2
ln
3
-
3
(
1
-
3
)
ln
2
+
2
3
ln
(
1
+
3
)
}
⋅
γ
-
2
3
(
3
ln
2
+
ln
3
+
ln
π
)
⋅
ln
(
1
+
3
)
-
7
-
6
3
2
ln
2
2
-
3
4
ln
2
3
+
3
3
(
1
-
3
)
2
ln
3
⋅
ln
2
+
3
ln
2
⋅
ln
π
-
π
(
17
+
8
3
)
2
3
ln
2
+
π
(
1
-
3
)
3
4
ln
3
-
π
3
(
2
+
3
)
ln
π
=
-
29.84287823
…
Doc 12
1.0000
-20.0000
2.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dedekind_eta_function.html
j
2
A
(
-
58
2
)
=
396
4
,
e
π
58
≈
396
4
-
104.00000017
…
Doc 13
1.0000
-21.0000
2.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Riemann–Siegel_theta_function.html
θ
′
(
0
)
=
-
ln
π
+
γ
+
π
/
2
+
3
ln
2
2
=
-
2.6860917
…
Doc 14
1.0000
-21.0000
2.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
ζ
′
(
2
)
= Derivative of
ζ
(
2
)
=
-
∑
n
=
2
∞
ln
n
n
2
=
-
0.9375482543
…
Doc 15
1.0000
-27.0000
2.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Madelung_constant.html
M
=
-
6
+
12
/
2
-
8
/
3
+
6
/
2
-
24
/
5
+
⋯
=
-
1.74756
…
.
Doc 16
0.5714
-17.0000
1.0000
0.5714
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Misiurewicz_point.html
{
0
,
i
,
i
-
1
,
-
i
,
i
-
1
,
-
i
…
}
Doc 17
0.5714
-43.0000
1.0000
0.5714
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Random_Fibonacci_sequence.html
1
,
1
,
2
,
3
,
1
,
-
2
,
-
3
,
-
5
,
-
2
,
-
3
,
…
for the signs
+
,
+
,
+
,
-
,
-
,
+
,
-
,
-
,
…
.
Doc 18
0.5714
-47.0000
0.0000
1.7143
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Heegner_number.html
e
π
19
≈
(
5
x
)
3
-
6.000 010
…
e
π
43
≈
(
5
x
)
3
-
6.000 000 010
…
e
π
67
≈
(
5
x
)
3
-
6.000 000 000 061
…
e
π
163
≈
(
5
x
)
3
-
6.000 000 000 000 000 034
…
e
π
163
=
(
e
π
i
/
24
η
(
τ
)
η
(
2
τ
)
)
24
-
24.000 000 000 000 001 05
…
e
π
163
=
(
e
π
i
/
12
η
(
τ
)
η
(
3
τ
)
)
12
-
12.000 000 000 000 000 21
…
e
π
163
=
(
e
π
i
/
6
η
(
τ
)
η
(
5
τ
)
)
6
-
6.000 000 000 000 000 034
…
e
π
19
≈
3
5
(
3
-
2
(
-
3
+
1
3
⋅
19
)
)
-
2
-
12.000 06
…
e
π
43
≈
3
5
(
9
-
2
(
-
39
+
7
3
⋅
43
)
)
-
2
-
12.000 000 061
…
e
π
67
≈
3
5
(
21
-
2
(
-
219
+
31
3
⋅
67
)
)
-
2
-
12.000 000 000 36
…
e
π
163
≈
3
5
(
231
-
2
(
-
26 679
+
2 413
3
⋅
163
)
)
-
2
-
12.000 000 000 000 000 21
…
Doc 19
0.5714
-82.0000
1.0000
0.5714
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html
(
-
n
k
)
=
-
n
⋅
-
(
n
+
1
)
…
-
(
n
+
k
-
2
)
⋅
-
(
n
+
k
-
1
)
k
!
=
(
-
1
)
k
n
⋅
(
n
+
1
)
⋅
(
n
+
2
)
⋯
(
n
+
k
-
1
)
k
!
=
(
-
1
)
k
(
n
+
k
-
1
k
)
=
(
-
1
)
k
(
(
n
k
)
)
.
Doc 20
0.3636
-10.0000
2.0000
0.7273
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Golden_ratio.html
φ
=
1
-
5
2
=
-
0.6180 339887
…
-
1
φ
=
1
-
φ
=
1
-
5
2
=
-
0.61803 39887
…
.
Doc 21
0.3636
-12.0000
2.0000
0.3636
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Field_electron_emission.html
ϵ
n
=
ϵ
-
K
p
…
…
…
.
.
(
16
)
Doc 22
0.3636
-22.0000
2.0000
0.3636
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Duckworth–Lewis_method.html
Total
resources
available
=
Resources
at start
of innings
-
Resources lost by
first interruption
-
Resources lost by
second interruption
-
Resources lost by
third interruption
-
etc
…
Doc 23
0.3636
-29.0000
2.0000
0.3636
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Power_series_solution_of_differential_equations.html
c
2
=
-
1
6
;
c
3
=
-
1
108
;
c
4
=
7
3240
;
c
5
=
-
19
48600
…
Doc 24
0.3636
-37.0000
2.0000
0.3636
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Joint_entropy.html
H
(
X
1
,
…
,
X
n
)
=
-
∑
x
1
…
∑
x
n
P
(
x
1
,
…
,
x
n
)
log
2
[
P
(
x
1
,
…
,
x
n
)
]