tangent
Not Supported
∫
ℝ
n
f
d
x
=
∫
0
∞
{
∫
x0
f
d
S
}
d
r
.
Search
Returned 85 matches (100 formulae, 141 docs)
Lookup 4235.370 ms, Re-ranking 852.333 ms
Found 105803858 tuple postings, 7989327 formulae, 3669233 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
Doc 1
0.4819
-8.0000
7.0000
0.4819
testing/NTCIR/xhtml5/5/0806.2921/0806.2921_1_23.xhtml
∫
S
f
d
λ
=
∫
0
∞
f
(
r
)
A
(
r
)
d
r
,
Doc 2
0.4586
-7.0000
5.0000
0.4586
testing/NTCIR/xhtml5/8/1209.6413/1209.6413_1_2.xhtml
∫
Ω
x
(
∫
ℝ
n
f
d
v
-
1
)
d
x
=
0
Doc 3
0.4586
-22.0000
8.0000
0.4586
testing/NTCIR/xhtml5/7/1007.5248/1007.5248_1_218.xhtml
∫
ℝ
n
f
d
σ
=
∫
0
+
∞
∫
S
f
(
ϵ
t
(
ω
)
)
d
τ
(
ω
)
t
Q
δ
-
1
d
t
.
Doc 4
0.4271
-2.0000
7.0000
0.4271
testing/NTCIR/xhtml5/9/1211.7303/1211.7303_1_33.xhtml
∫
Ω
f
d
x
=
∫
Γ
d
d
S
Doc 5
0.4271
-4.0000
7.0000
0.4271
testing/NTCIR/xhtml5/6/0907.1806/0907.1806_1_64.xhtml
lim
∫
ℝ
f
d
ν
k
=
∫
ℝ
f
d
μ
Doc 6
0.4271
-6.0000
9.0000
0.4271
testing/NTCIR/xhtml5/2/math-ph0204032/math-ph0204032_1_81.xhtml
∫
ℝ
n
f
d
x
=
∫
ℝ
n
g
d
x
=
1
Doc 7
0.4271
-8.0000
6.0000
0.4271
testing/NTCIR/xhtml5/4/math0702456/math0702456_1_58.xhtml
lim
n
→
∞
∫
ℂ
f
d
τ
n
=
∫
ℝ
f
d
μ
K
Doc 8
0.4271
-9.0000
7.0000
0.4271
testing/NTCIR/xhtml5/3/math0310377/math0310377_1_16.xhtml
lim
n
→
∞
∫
ℝ
d
f
d
ν
n
=
∫
ℝ
d
f
d
μ
Doc 9
0.4043
-6.0000
4.0000
0.4043
testing/NTCIR/xhtml5/2/hep-th0108026/hep-th0108026_1_5.xhtml
M
=
∫
0
∞
(
ℛ
-
1
)
r
2
d
r
.
Doc 10
0.4043
-6.0000
4.0000
0.4043
testing/NTCIR/xhtml5/1/hep-th9910171/hep-th9910171_1_9.xhtml
M
=
∫
0
∞
(
ℛ
-
1
)
r
2
d
r
.
Doc 11
0.3913
-4.0000
8.0000
0.3913
testing/NTCIR/xhtml5/6/0911.3404/0911.3404_1_74.xhtml
∫
ℝ
u
d
x
=
∫
ℝ
u
0
d
x
.
Doc 12
0.3913
-4.0000
8.0000
0.3913
testing/NTCIR/xhtml5/6/0911.3404/0911.3404_1_34.xhtml
∫
ℝ
u
d
x
=
∫
ℝ
u
0
d
x
.
Doc 13
0.3721
-4.0000
7.0000
0.3721
testing/NTCIR/xhtml5/6/1003.5248/1003.5248_1_51.xhtml
∫
H
f
d
x
=
∫
H
c
f
d
x
Doc 14
0.3721
-4.0000
7.0000
0.3721
testing/NTCIR/xhtml5/6/1003.5248/1003.5248_1_53.xhtml
∫
B
f
d
x
=
∫
B
c
f
d
x
Doc 15
0.3721
-4.0000
7.0000
0.3721
testing/NTCIR/xhtml5/6/1003.5248/1003.5248_1_22.xhtml
∫
B
f
d
x
=
∫
B
c
f
d
x
Doc 16
0.3721
-6.0000
7.0000
0.3721
testing/NTCIR/xhtml5/6/1003.5248/1003.5248_1_31.xhtml
∫
B
f
d
x
=
∫
ℝ
N
∖
B
f
d
x
Doc 17
0.3721
-6.0000
7.0000
0.3721
testing/NTCIR/xhtml5/6/1003.5248/1003.5248_1_32.xhtml
∫
H
f
d
x
=
∫
ℝ
N
∖
H
f
d
x
Doc 18
0.3721
-6.0000
7.0000
0.3721
testing/NTCIR/xhtml5/6/1003.5248/1003.5248_1_33.xhtml
∫
B
f
d
x
=
∫
ℝ
N
∖
B
f
d
x
Doc 19
0.3721
-7.0000
7.0000
0.3721
testing/NTCIR/xhtml5/7/1104.4479/1104.4479_1_29.xhtml
∫
0
∞
τ
x
f
d
μ
=
∫
0
∞
f
d
μ
Doc 20
0.3721
-8.0000
7.0000
0.3721
testing/NTCIR/xhtml5/6/0904.4275/0904.4275_1_18.xhtml
∫
B
f
p
d
x
=
∫
ℝ
N
∖
B
f
p
d
x
Doc 21
0.3721
-8.0000
7.0000
0.3721
testing/NTCIR/xhtml5/6/0904.4275/0904.4275_1_19.xhtml
∫
H
f
p
d
x
=
∫
ℝ
N
∖
H
f
p
d
x
Doc 22
0.3721
-8.0000
7.0000
0.3721
testing/NTCIR/xhtml5/6/0906.1470/0906.1470_1_116.xhtml
∫
Ω
f
k
d
x
=
∫
Ω
f
¯
k
d
x
=
0
Doc 23
0.3721
-8.0000
7.0000
0.3721
testing/NTCIR/xhtml5/6/0904.4275/0904.4275_1_20.xhtml
∫
B
f
p
d
x
=
∫
ℝ
N
∖
B
f
p
d
x
Doc 24
0.3721
-11.0000
7.0000
0.3721
testing/NTCIR/xhtml5/6/0904.0583/0904.0583_1_37.xhtml
∫
E
∩
H
-
f
d
x
=
∫
E
∩
H
+
f
d
x
=
0
Doc 25
0.3500
-2.0000
6.0000
0.3500
testing/NTCIR/xhtml5/7/1104.1271/1104.1271_1_14.xhtml
∫
ℝ
n
u
0
d
x
=
0
Doc 26
0.3500
-2.0000
6.0000
0.3500
testing/NTCIR/xhtml5/7/1104.1271/1104.1271_1_86.xhtml
∫
ℝ
n
u
0
d
x
=
0
Doc 27
0.3500
-10.0000
7.0000
0.3500
testing/NTCIR/xhtml5/5/0707.1084/0707.1084_1_45.xhtml
F
=
∫
f
d
0
x
=
∫
-
∞
∞
f
d
x
X
Doc 28
0.3500
-12.0000
6.0000
0.3500
testing/NTCIR/xhtml5/10/gr-qc9809058/gr-qc9809058_1_19.xhtml
F
=
∫
Ω
f
d
n
x
=
∫
ℝ
n
θ
Ω
f
d
n
x
,
Doc 29
0.3500
-15.0000
6.0000
0.3500
testing/NTCIR/xhtml5/8/1204.1667/1204.1667_1_53.xhtml
∫
ℝ
n
|
f
|
p
w
d
x
=
∫
0
∞
f
w
*
(
t
)
p
d
t
.
Doc 30
0.3347
-3.0000
8.0000
0.3347
testing/NTCIR/xhtml5/8/1210.5930/1210.5930_1_11.xhtml
∫
f
d
x
=
∫
Ω
f
d
x
.
Doc 31
0.3347
-3.0000
8.0000
0.3347
testing/NTCIR/xhtml5/8/1210.6493/1210.6493_1_6.xhtml
∫
f
d
x
=
∫
Ω
f
d
x
.
Doc 32
0.3347
-4.0000
8.0000
0.3347
testing/NTCIR/xhtml5/7/1004.4749/1004.4749_1_5.xhtml
∫
f
d
x
=
∫
ℝ
3
f
d
x
.
Doc 33
0.3347
-4.0000
8.0000
0.3347
testing/NTCIR/xhtml5/8/1111.2114/1111.2114_1_9.xhtml
∫
f
d
x
=
∫
ℝ
3
f
d
x
.
Doc 34
0.3347
-4.0000
8.0000
0.3347
testing/NTCIR/xhtml5/8/1207.3746/1207.3746_1_5.xhtml
∫
f
d
x
=
∫
ℝ
2
f
d
x
.
Doc 35
0.3347
-10.0000
7.0000
0.3347
testing/NTCIR/xhtml5/5/0806.0021/0806.0021_1_55.xhtml
=
∫
ℝ
n
f
+
d
γ
n
+
∫
ℝ
n
f
-
d
γ
n
Doc 36
0.3167
-2.0000
5.0000
0.3167
testing/NTCIR/xhtml5/5/0710.4324/0710.4324_1_2.xhtml
J
=
∫
0
∞
f
k
d
x
Doc 37
0.3167
-8.0000
6.0000
0.3167
testing/NTCIR/xhtml5/9/1307.3989/1307.3989_1_17.xhtml
lim
n
→
∞
∫
f
d
μ
n
=
∫
f
d
μ
0
Doc 38
0.3167
-15.0000
5.0000
0.3167
testing/NTCIR/xhtml5/4/math0604554/math0604554_1_71.xhtml
∫
0
∞
p
t
p
-
1
|
E
t
|
d
t
=
∫
ℝ
n
f
p
d
x
.
Doc 39
0.3167
-16.0000
6.0000
0.3167
testing/NTCIR/xhtml5/6/0910.2591/0910.2591_1_20.xhtml
lim
i
→
∞
∫
f
d
μ
i
=
∫
f
d
μ
for all
f
∈
C
c
(
ℝ
n
)
.
Doc 40
0.2956
-1.0000
6.0000
0.5911
testing/NTCIR/xhtml5/5/0811.4673/0811.4673_1_263.xhtml
∫
ℝ
f
d
x
=
0
∫
ℝ
f
1
d
x
=
-
∫
ℝ
f
2
d
x
≠
0
Doc 41
0.2956
-1.0000
5.0000
0.2956
testing/NTCIR/xhtml5/5/0810.3073/0810.3073_1_58.xhtml
∫
B
f
d
x
=
0
Doc 42
0.2956
-1.0000
5.0000
0.2956
testing/NTCIR/xhtml5/6/0904.0583/0904.0583_1_34.xhtml
∫
P
f
d
x
=
0
Doc 43
0.2956
-1.0000
5.0000
0.2956
testing/NTCIR/xhtml5/8/1211.4408/1211.4408_1_12.xhtml
∫
𝒪
f
d
x
=
0
Doc 44
0.2956
-1.0000
5.0000
0.2956
testing/NTCIR/xhtml5/6/0904.0583/0904.0583_1_32.xhtml
∫
P
f
d
x
=
0
Doc 45
0.2956
-1.0000
5.0000
0.2956
testing/NTCIR/xhtml5/6/0904.0583/0904.0583_1_61.xhtml
∫
P
f
d
x
=
0
Doc 46
0.2956
-1.0000
5.0000
0.2956
testing/NTCIR/xhtml5/7/1011.5863/1011.5863_1_144.xhtml
∫
B
f
d
x
=
0
Doc 47
0.2956
-1.0000
5.0000
0.2956
testing/NTCIR/xhtml5/6/0904.0583/0904.0583_1_31.xhtml
∫
P
f
d
x
=
0
Doc 48
0.2956
-1.0000
5.0000
0.2956
testing/NTCIR/xhtml5/8/1108.2249/1108.2249_1_28.xhtml
∫
𝐓
f
d
x
=
0
Doc 49
0.2956
-2.0000
6.0000
0.2956
testing/NTCIR/xhtml5/9/1212.5066/1212.5066_1_2.xhtml
∫
ℝ
2
f
d
x
=
0
Doc 50
0.2956
-2.0000
6.0000
0.2956
testing/NTCIR/xhtml5/6/1002.2489/1002.2489_1_28.xhtml
∫
ℝ
f
d
x
h
=
0
Doc 51
0.2956
-4.0000
5.0000
0.2956
testing/NTCIR/xhtml5/4/math0606060/math0606060_1_9.xhtml
ν
(
f
)
=
∫
ℝ
n
f
d
ν
Doc 52
0.2956
-4.0000
5.0000
0.2956
testing/NTCIR/xhtml5/8/1209.6413/1209.6413_1_8.xhtml
Δ
x
Φ
=
∫
ℝ
n
f
d
v
Doc 53
0.2956
-5.0000
6.0000
0.2956
testing/NTCIR/xhtml5/3/math0412208/math0412208_1_102.xhtml
lim
m
→
∞
∫
ℝ
n
f
m
d
x
Doc 54
0.2956
-10.0000
5.0000
0.2956
testing/NTCIR/xhtml5/7/1009.3046/1009.3046_1_18.xhtml
∫
Ω
x
(
1
-
∫
ℝ
n
f
d
v
)
d
x
=
0
Doc 55
0.2956
-10.0000
5.0000
0.2956
testing/NTCIR/xhtml5/6/0901.1068/0901.1068_1_2.xhtml
∫
ℝ
n
ρ
(
t
)
d
x
=
∫
ℝ
n
ρ
0
d
x
Doc 56
0.2956
-10.0000
5.0000
0.2956
testing/NTCIR/xhtml5/4/math0608379/math0608379_1_41.xhtml
∫
ℝ
n
L
0
f
d
μ
≤
ω
∫
ℝ
n
f
d
μ
Doc 57
0.2956
-10.0000
5.0000
0.2956
testing/NTCIR/xhtml5/8/1111.3306/1111.3306_1_33.xhtml
-
ρ
ε
=
-
∫
Ω
∫
ℝ
n
f
d
ζ
d
x
.
Doc 58
0.2956
-13.0000
6.0000
0.2956
testing/NTCIR/xhtml5/8/1206.1963/1206.1963_1_11.xhtml
∫
ℝ
2
F
(
u
)
d
x
=
∫
0
∞
F
(
u
*
)
d
s
.
Doc 59
0.2956
-13.0000
6.0000
0.2956
testing/NTCIR/xhtml5/8/1206.1963/1206.1963_1_10.xhtml
∫
ℝ
2
F
(
u
)
d
x
=
∫
0
∞
F
(
u
*
)
d
s
.
Doc 60
0.2956
-14.0000
6.0000
0.2956
testing/NTCIR/xhtml5/7/1004.2445/1004.2445_1_75.xhtml
∫
0
∞
f
[
ϕ
(
x
)
]
d
x
=
∫
0
∞
f
(
x
)
d
x
.
Doc 61
0.2956
-17.0000
6.0000
0.2956
testing/NTCIR/xhtml5/4/math0602658/math0602658_1_3.xhtml
∫
0
∞
q
n
f
(
x
)
d
q
x
=
∫
0
∞
f
(
x
)
d
q
x
.
Doc 62
0.2956
-23.0000
6.0000
0.2956
testing/NTCIR/xhtml5/5/0809.3315/0809.3315_1_1.xhtml
∫
ℝ
n
f
(
x
)
d
x
=
∫
0
∞
∫
Σ
f
(
A
t
θ
)
t
γ
-
1
d
σ
(
θ
)
d
t
Doc 63
0.2956
-24.0000
6.0000
0.2956
testing/NTCIR/xhtml5/8/1208.2839/1208.2839_1_13.xhtml
∫
G
f
(
x
)
d
x
=
∫
0
∞
∫
S
1
f
(
D
r
x
)
d
σ
(
x
)
r
Q
-
1
d
r
.
Doc 64
0.2956
-25.0000
6.0000
0.2956
testing/NTCIR/xhtml5/4/math0602664/math0602664_1_13.xhtml
∫
ℝ
d
f
(
x
)
d
x
=
∫
0
∞
∫
S
0
f
(
r
E
θ
)
σ
(
d
θ
)
r
q
-
1
d
r
.
Doc 65
0.2956
-26.0000
6.0000
0.2956
testing/NTCIR/xhtml5/4/math0702050/math0702050_1_20.xhtml
∫
ℝ
d
f
(
x
)
d
x
=
∫
0
∞
∫
S
E
f
(
r
E
θ
)
σ
E
(
d
θ
)
r
q
-
1
d
r
.
Doc 66
0.2909
-5.0000
7.0000
0.2909
testing/NTCIR/xhtml5/4/math0606126/math0606126_1_69.xhtml
∫
S
f
k
d
x
→
∫
S
f
d
x
.
Doc 67
0.2909
-6.0000
6.0000
0.2909
testing/NTCIR/xhtml5/6/0912.2193/0912.2193_1_96.xhtml
∫
S
f
n
d
μ
n
→
∫
S
f
d
μ
.
Doc 68
0.2609
-5.0000
4.0000
0.2609
testing/NTCIR/xhtml5/3/math-ph0302019/math-ph0302019_1_83.xhtml
I
=
∫
0
∞
g
(
x
)
d
x
.
Doc 69
0.2609
-5.0000
4.0000
0.2609
testing/NTCIR/xhtml5/5/0801.1130/0801.1130_1_63.xhtml
ι
=
∫
B
5
(
0
)
f
d
x
.
Doc 70
0.2609
-6.0000
4.0000
0.2609
testing/NTCIR/xhtml5/8/1111.2657/1111.2657_1_7.xhtml
∫
ℝ
3
f
=
∫
ℝ
3
f
d
x
.
Doc 71
0.2609
-7.0000
4.0000
0.2609
testing/NTCIR/xhtml5/3/cond-mat0409566/cond-mat0409566_1_48.xhtml
M
n
=
∫
0
∞
f
(
x
)
x
n
d
x
Doc 72
0.2609
-7.0000
4.0000
0.2609
testing/NTCIR/xhtml5/8/1205.2223/1205.2223_1_60.xhtml
=
∫
0
∞
∫
ℝ
g
φ
d
x
d
t
,
Doc 73
0.2609
-7.0000
4.0000
0.2609
testing/NTCIR/xhtml5/3/cond-mat0409566/cond-mat0409566_1_19.xhtml
M
n
=
∫
0
∞
f
(
x
)
x
n
d
x
Doc 74
0.2609
-7.0000
4.0000
0.2609
testing/NTCIR/xhtml5/3/cond-mat0409566/cond-mat0409566_1_49.xhtml
M
n
=
∫
0
∞
f
(
x
)
x
n
d
x
Doc 75
0.2609
-8.0000
4.0000
0.2609
testing/NTCIR/xhtml5/2/hep-th0110245/hep-th0110245_1_12.xhtml
M
=
∫
0
∞
r
2
(
1
-
ℛ
)
d
r
.
Doc 76
0.2609
-8.0000
4.0000
0.2609
testing/NTCIR/xhtml5/2/hep-th0110245/hep-th0110245_1_11.xhtml
L
=
∫
0
∞
r
2
(
ℛ
-
1
)
d
r
.
Doc 77
0.2609
-11.0000
3.0000
0.5018
testing/NTCIR/xhtml5/7/1107.4663/1107.4663_1_6.xhtml
∫
0
T
∫
f
=
∫
0
T
∫
Ω
f
d
x
d
t
.
∫
f
=
∫
Ω
f
d
x
Doc 78
0.2609
-11.0000
3.0000
0.5018
testing/NTCIR/xhtml5/7/1107.4663/1107.4663_1_9.xhtml
∫
0
T
∫
f
=
∫
0
T
∫
Ω
f
d
x
d
t
.
∫
f
=
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Ω
f
d
x
Doc 79
0.2410
-1.0000
3.0000
0.2410
testing/NTCIR/xhtml5/8/1203.0326/1203.0326_1_71.xhtml
∫
0
∞
f
d
μ
Doc 80
0.2410
-5.0000
5.0000
0.2410
testing/NTCIR/xhtml5/5/0801.1277/0801.1277_1_79.xhtml
P
0
f
=
∫
ℝ
2
f
d
x
Doc 81
0.2410
-6.0000
4.0000
0.2410
testing/NTCIR/xhtml5/5/0810.3538/0810.3538_1_119.xhtml
∫
0
∞
Z
x
d
x
=
+
∞
.
Doc 82
0.2410
-6.0000
4.0000
0.2410
testing/NTCIR/xhtml5/8/1206.6144/1206.6144_1_19.xhtml
∫
f
d
x
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∫
Ω
f
d
x
.
Doc 83
0.2410
-6.0000
3.0000
0.4450
testing/NTCIR/xhtml5/7/1106.4724/1106.4724_1_32.xhtml
∫
ℝ
n
T
f
(
x
)
d
x
=
0
∫
ℝ
n
f
(
x
)
d
x
=
0
Doc 84
0.2410
-6.0000
3.0000
0.2410
testing/NTCIR/xhtml5/7/1106.4724/1106.4724_1_52.xhtml
∫
ℝ
n
T
f
(
x
)
d
x
=
0
Doc 85
0.2410
-6.0000
3.0000
0.2410
testing/NTCIR/xhtml5/7/1106.4724/1106.4724_1_65.xhtml
∫
ℝ
n
T
f
(
x
)
d
x
=
0
Doc 86
0.2410
-6.0000
3.0000
0.2410
testing/NTCIR/xhtml5/7/1106.4724/1106.4724_1_50.xhtml
∫
ℝ
n
T
f
(
x
)
d
x
=
0
Doc 87
0.2410
-6.0000
3.0000
0.2410
testing/NTCIR/xhtml5/7/1106.4724/1106.4724_1_49.xhtml
∫
ℝ
n
T
f
(
x
)
d
x
=
0
Doc 88
0.2410
-8.0000
2.0000
0.2410
testing/NTCIR/xhtml5/5/0811.4601/0811.4601_1_133.xhtml
∫
0
∞
∫
ℝ
d
m
f
m
d
x
d
m
Doc 89
0.2410
-14.0000
5.0000
0.2410
testing/NTCIR/xhtml5/8/1111.1680/1111.1680_1_49.xhtml
∫
ℝ
3
f
(
|
x
|
)
d
x
=
∫
-
∞
∞
f
(
r
)
d
r
;
Doc 90
0.2410
-14.0000
5.0000
0.2410
testing/NTCIR/xhtml5/8/1111.1680/1111.1680_1_48.xhtml
∫
ℝ
3
f
(
|
x
|
)
d
x
=
∫
-
∞
∞
f
(
r
)
d
r
;
Doc 91
0.2410
-15.0000
4.0000
0.2410
testing/NTCIR/xhtml5/7/1004.1618/1004.1618_1_23.xhtml
∫
ℝ
n
P
(
f
)
g
d
x
=
∫
ℝ
n
f
P
(
g
)
d
x
.
Doc 92
0.2410
-19.0000
4.0000
0.2410
testing/NTCIR/xhtml5/8/1204.6540/1204.6540_1_84.xhtml
∫
Ω
∫
ℝ
2
f
d
𝐯
d
x
=
∫
Ω
∫
ℝ
2
f
0
d
𝐯
d
x
=
0.
Doc 93
0.2410
-21.0000
5.0000
0.2410
testing/NTCIR/xhtml5/4/math0510590/math0510590_1_103.xhtml
lim
n
→
+
∞
∫
ℝ
2
u
n
1
Ω
n
b
f
d
x
=
∫
Ω
φ
b
f
d
x
.
Doc 94
0.2182
-5.0000
4.0000
0.2182
testing/NTCIR/xhtml5/2/math0202255/math0202255_1_5.xhtml
∫
ℝ
n
f
(
x
)
d
x
=
+
∞
Doc 95
0.2182
-7.0000
4.0000
0.2182
testing/NTCIR/xhtml5/2/hep-th0212086/hep-th0212086_1_18.xhtml
E
[
σ
]
=
∫
0
∞
ϵ
(
r
)
d
r
.
Doc 96
0.2041
-3.0000
3.0000
0.2041
testing/NTCIR/xhtml5/5/0707.0974/0707.0974_1_176.xhtml
∫
0
∞
f
*
f
d
x
Doc 97
0.2041
-4.0000
4.0000
0.2041
testing/NTCIR/xhtml5/6/0905.1794/0905.1794_1_7.xhtml
∫
ℝ
n
f
0
(
x
)
d
x
Doc 98
0.2041
-5.0000
4.0000
0.2041
testing/NTCIR/xhtml5/2/math0201301/math0201301_1_2.xhtml
∫
ℝ
n
f
(
x
)
d
x
=
0
Doc 99
0.2041
-5.0000
4.0000
0.2041
testing/NTCIR/xhtml5/5/0805.1807/0805.1807_1_26.xhtml
∫
ℝ
n
f
(
x
)
d
x
=
1
Doc 100
0.2041
-5.0000
4.0000
0.2041
testing/NTCIR/xhtml5/2/math-ph0202042/math-ph0202042_1_136.xhtml
∫
ℝ
n
f
(
x
)
d
x
=
1
Doc 101
0.2041
-5.0000
4.0000
0.2041
testing/NTCIR/xhtml5/5/0804.1553/0804.1553_1_9.xhtml
∫
ℝ
n
f
(
x
)
d
x
=
1
Doc 102
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/7/1103.1715/1103.1715_1_3.xhtml
∫
ℝ
n
φ
(
x
)
d
x
=
0
Doc 103
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/7/1103.1715/1103.1715_1_2.xhtml
∫
ℝ
n
ψ
(
x
)
d
x
=
0
Doc 104
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/8/1210.5795/1210.5795_1_3.xhtml
∫
ℝ
n
φ
(
x
)
d
x
=
0
Doc 105
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/7/1102.5467/1102.5467_1_45.xhtml
∫
ℝ
n
m
(
x
)
d
x
=
0
Doc 106
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/8/1111.1387/1111.1387_1_2.xhtml
∫
ℝ
n
ψ
(
x
)
d
x
=
0
Doc 107
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/1/1207.1242/1207.1242_1_2.xhtml
∫
ℝ
n
ψ
(
x
)
d
x
=
0
Doc 108
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/1/1207.1242/1207.1242_1_30.xhtml
∫
ℝ
n
b
(
x
)
d
x
=
0
Doc 109
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/8/1111.1387/1111.1387_1_3.xhtml
∫
ℝ
n
φ
(
x
)
d
x
=
0
Doc 110
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/7/1102.5467/1102.5467_1_42.xhtml
∫
ℝ
n
a
(
x
)
d
x
=
0
Doc 111
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/7/1006.0562/1006.0562_1_150.xhtml
∫
ℝ
n
Ψ
(
x
)
d
x
=
0
Doc 112
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/8/1210.5795/1210.5795_1_2.xhtml
∫
ℝ
n
ψ
(
x
)
d
x
=
0
Doc 113
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/1/1207.1242/1207.1242_1_38.xhtml
∫
ℝ
n
b
(
x
)
d
x
=
0
Doc 114
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/7/1010.0862/1010.0862_1_24.xhtml
∫
ℝ
n
φ
(
x
)
d
x
=
0
Doc 115
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/1/1207.1242/1207.1242_1_3.xhtml
∫
ℝ
n
φ
(
x
)
d
x
=
0
Doc 116
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/7/1010.1132/1010.1132_1_26.xhtml
∫
ℝ
n
φ
(
x
)
d
x
=
0
Doc 117
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/1/1102.4380/1102.4380_1_2.xhtml
∫
ℝ
n
ψ
(
x
)
d
x
=
0
Doc 118
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/1/1102.4380/1102.4380_1_3.xhtml
∫
ℝ
n
φ
(
x
)
d
x
=
0
Doc 119
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/7/1103.3757/1103.3757_1_196.xhtml
∫
ℝ
n
a
(
x
)
d
x
=
0
Doc 120
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/9/1401.6617/1401.6617_1_1.xhtml
∫
ℝ
n
φ
(
x
)
d
x
=
0
Doc 121
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/7/1104.1271/1104.1271_1_82.xhtml
∫
ℝ
n
ϕ
(
x
)
d
x
=
0
Doc 122
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/9/1312.5587/1312.5587_1_7.xhtml
∫
ℝ
n
ϕ
(
x
)
d
x
=
0
Doc 123
0.2041
-5.0000
3.0000
0.2041
testing/NTCIR/xhtml5/7/1010.1706/1010.1706_1_17.xhtml
∫
ℝ
n
φ
(
x
)
d
x
=
0
Doc 124
0.2041
-6.0000
4.0000
0.2041
testing/NTCIR/xhtml5/6/0905.1794/0905.1794_1_4.xhtml
∫
ℝ
n
f
0
(
x
)
d
x
=
1
Doc 125
0.2041
-6.0000
4.0000
0.2041
testing/NTCIR/xhtml5/8/1206.2130/1206.2130_1_18.xhtml
μ
=
∫
ℝ
n
f
(
v
)
d
v
.
Doc 126
0.2041
-7.0000
4.0000
0.2041
testing/NTCIR/xhtml5/7/1004.1618/1004.1618_1_42.xhtml
∫
ℝ
n
f
0
(
x
)
d
x
=
0
;
Doc 127
0.2041
-13.0000
5.0000
0.2041
testing/NTCIR/xhtml5/5/math0703857/math0703857_1_117.xhtml
1
n
=
∫
0
∞
f
(
r
x
)
r
n
-
1
d
r
.
Doc 128
0.2041
-14.0000
3.0000
0.2041
testing/NTCIR/xhtml5/5/0712.1090/0712.1090_1_19.xhtml
∫
ℝ
f
(
x
,
t
)
d
x
=
∫
ℝ
f
0
(
x
)
d
x
.
Doc 129
0.2041
-16.0000
4.0000
0.2041
testing/NTCIR/xhtml5/8/1112.3073/1112.3073_1_39.xhtml
x
0
=
∫
ℝ
n
x
f
(
x
)
d
x
/
∫
ℝ
n
f
(
x
)
d
x
Doc 130
0.2041
-16.0000
4.0000
0.2041
testing/NTCIR/xhtml5/6/0906.2448/0906.2448_1_28.xhtml
π
f
(
S
)
=
∫
S
f
(
x
)
d
x
/
∫
ℝ
n
f
(
x
)
d
x
Doc 131
0.1860
-10.0000
3.0000
0.1860
testing/NTCIR/xhtml5/6/0909.3742/0909.3742_1_33.xhtml
∫
0
∞
M
=
∫
ℝ
n
m
≤
(
1
+
ε
)
Doc 132
0.1562
-17.0000
4.0000
0.1562
testing/NTCIR/xhtml5/3/math0406251/math0406251_1_74.xhtml
∫
ℝ
2
f
(
|
x
|
)
d
2
x
=
2
π
∫
0
∞
f
(
r
)
r
d
r
.
Doc 133
0.1455
-5.0000
3.0000
0.1455
testing/NTCIR/xhtml5/8/1110.0333/1110.0333_1_131.xhtml
∫
0
∞
f
n
(
x
)
d
x
Doc 134
0.1455
-6.0000
3.0000
0.1455
testing/NTCIR/xhtml5/5/0708.1866/0708.1866_1_14.xhtml
∫
0
∞
f
(
x
)
d
x
=
1
Doc 135
0.1455
-6.0000
3.0000
0.1455
testing/NTCIR/xhtml5/5/0708.3761/0708.3761_1_12.xhtml
∫
0
∞
f
(
x
)
d
x
=
1
Doc 136
0.1455
-6.0000
3.0000
0.1455
testing/NTCIR/xhtml5/3/math-ph0501003/math-ph0501003_1_26.xhtml
∫
0
∞
f
(
x
)
d
x
=
1
Doc 137
0.1455
-6.0000
3.0000
0.1455
testing/NTCIR/xhtml5/4/cond-mat0510064/cond-mat0510064_1_36.xhtml
∫
0
∞
f
(
x
)
d
x
=
1
Doc 138
0.1455
-6.0000
3.0000
0.1455
testing/NTCIR/xhtml5/8/1210.0291/1210.0291_1_25.xhtml
∫
0
∞
f
(
x
)
d
x
=
1
Doc 139
0.1455
-6.0000
3.0000
0.1455
testing/NTCIR/xhtml5/3/cond-mat0409566/cond-mat0409566_1_2.xhtml
∫
0
∞
f
(
x
)
d
x
=
1
Doc 140
0.1455
-7.0000
3.0000
0.1455
testing/NTCIR/xhtml5/4/math0702806/math0702806_1_111.xhtml
∫
0
∞
ψ
(
x
)
d
x
=
∞
.
Doc 141
0.1455
-7.0000
2.0000
0.1455
testing/NTCIR/xhtml5/2/math-ph0101008/math-ph0101008_1_35.xhtml
∫
-
∞
∞
f
(
x
)
d
x
=
0