tangent
Not Supported
f
μ
=
-
8
π
G
3
c
4
(
A
2
T
α
β
+
B
2
T
η
α
β
)
(
δ
ν
μ
+
u
μ
u
ν
)
u
α
x
ν
u
β
Search
Returned 97 matches (100 formulae, 73 docs)
Lookup 5.410 ms, Re-ranking 4492.517 ms
Found 69325 tuple postings, 48574 formulae, 11188 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
f
μ
=
-
8
π
G
3
c
4
(
A
2
T
α
β
+
B
2
T
η
α
β
)
(
δ
ν
μ
+
u
μ
u
ν
)
u
α
x
ν
u
β
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
f
´
μ
=
-
8
π
G
3
c
4
(
A
2
T
´
α
β
+
B
2
T
´
g
α
β
)
(
δ
ν
μ
+
u
´
μ
u
´
ν
)
u
´
α
x
´
ν
u
´
β
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
f
μ
=
-
8
π
G
3
c
4
(
A
2
T
α
β
+
B
2
T
η
α
β
)
δ
ν
μ
u
α
x
ν
u
β
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
R
´
α
β
=
8
π
G
c
4
(
A
2
T
´
α
β
+
B
2
T
´
g
α
β
)
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
R
´
=
R
´
α
α
=
8
π
G
c
4
(
A
2
T
´
α
α
+
B
2
T
´
δ
α
α
)
=
8
π
G
c
4
(
A
2
+
2
B
)
T
´
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
F
=
∫
(
A
2
ϕ
2
+
B
4
ϕ
4
+
κ
2
(
∇
ϕ
)
2
)
d
x
.
Doc 2
0.2447, -15.0000, 7.0000, 0.2447
testing/wikipedia/v3/17988.html
d
2
u
d
θ
2
+
u
=
r
s
c
2
2
h
2
+
3
r
s
2
u
2
-
G
Q
2
4
π
ε
0
c
4
(
c
2
h
2
u
+
2
u
3
)
Doc 3
0.2198, -38.0000, 5.0000, 0.2859
testing/wikipedia/v3/25303.html
Δ
ω
1
=
-
2
π
J
2
μ
p
2
3
2
(
3
2
sin
2
i
-
1
)
Doc 4
0.2118, -14.0000, 5.0000, 0.2118
testing/wikipedia/v3/26394.html
d
2
x
´
μ
d
τ
2
+
R
μ
´
α
ν
β
u
´
α
x
´
ν
u
´
β
=
0
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
R
α
β
-
1
2
R
g
α
β
+
g
α
β
Λ
=
8
π
G
c
4
μ
0
(
F
α
F
ψ
ψ
+
β
1
4
g
α
β
F
ψ
τ
F
ψ
τ
)
.
Doc 5
0.1983, -34.0000, 4.0000, 0.1983
testing/wikipedia/v3/04746.html
μ
0
l
2
π
(
ln
(
2
d
a
)
+
Y
2
)
Doc 6
0.1947, -8.0000, 5.0000, 0.1947
testing/wikipedia/v3/02526.html
T
00
→
u
α
(
A
T
α
β
+
B
T
η
α
β
)
u
β
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
d
u
μ
d
τ
+
R
μ
α
ν
β
u
α
x
ν
u
β
=
0
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
3
2
(
π
2
)
4
/
3
(
∫
d
𝐫
ρ
3
(
𝐫
)
)
1
/
3
≤
T
.
Doc 7
0.1782, -15.0000, 5.0000, 0.1782
testing/wikipedia/v3/10308.html
E
=
k
B
T
=
ℏ
g
2
π
c
=
ℏ
2
π
c
(
c
4
4
G
M
)
=
ℏ
c
3
8
π
G
M
Doc 8
0.1782, -25.0000, 3.0000, 0.1782
testing/wikipedia/v3/02637.html
λ
n
=
λ
u
2
γ
2
n
(
1
+
K
2
2
+
γ
2
θ
2
)
(
13
)
Doc 9
0.1696, -16.0000, 3.0000, 0.1696
testing/wikipedia/v3/02598.html
σ
(
B
)
-
σ
(
0
)
=
α
e
2
2
π
2
ℏ
(
l
n
(
B
ϕ
B
)
-
ψ
(
1
2
+
B
ϕ
B
)
)
Doc 10
0.1696, -27.0000, 2.0000, 0.1696
testing/wikipedia/v3/14407.html
d
S
α
d
τ
=
e
m
[
g
2
F
α
β
S
β
+
(
g
2
-
1
)
u
α
(
S
λ
F
λ
μ
U
μ
)
]
,
Doc 11
0.1696, -29.0000, 3.0000, 0.1696
testing/wikipedia/v3/11120.html
E
n
=
(
π
ℏ
β
D
α
1
/
α
q
2
/
β
2
B
(
1
β
,
1
α
+
1
)
)
α
β
α
+
β
(
n
+
1
2
)
α
β
α
+
β
.
Doc 12
0.1696, -40.0000, 5.0000, 0.1696
testing/wikipedia/v3/24344.html
f
μ
→
f
μ
+
u
μ
u
ν
f
ν
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
R
´
=
-
8
π
G
c
4
T
´
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
𝐟
=
-
4
π
G
3
c
4
(
M
c
2
V
)
𝐫
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
1
2
t
2
+
1
2
t
=
1
2
(
t
)
(
t
+
1
)
Doc 13
0.1597, -13.0000, 5.0000, 0.1597
testing/wikipedia/v3/05699.html
X
=
-
T
-
1
/
2
+
1
2
-
1
8
T
1
/
2
+
1
128
T
3
/
2
+
⋯
Doc 14
0.1597, -23.0000, 5.0000, 0.1597
testing/wikipedia/v3/10785.html
W
=
-
μ
J
m
2
ln
(
1
-
I
1
-
3
J
m
)
+
κ
2
(
J
2
-
1
2
-
ln
J
)
4
Doc 15
0.1597, -27.0000, 4.0000, 0.1597
testing/wikipedia/v3/25514.html
=
Z
D
P
2
ℏ
ω
8
π
2
ℏ
ρ
c
2
(
N
q
+
1
2
±
1
2
)
g
(
E
±
ℏ
ω
)
(
18
)
Doc 16
0.1597, -27.0000, 2.0000, 0.1597
testing/wikipedia/v3/23346.html
T
2
=
T
1
2
+
T
2
2
2
+
T
1
2
-
T
2
2
2
(
h
1
+
h
2
h
1
-
h
2
)
(
2
)
Doc 17
0.1597, -29.0000, 4.0000, 0.1597
testing/wikipedia/v3/02032.html
t
L
L
μ
ν
=
-
c
4
8
π
G
G
μ
ν
+
c
4
16
π
G
(
-
g
)
(
(
-
g
)
(
g
μ
ν
g
α
β
-
g
μ
α
g
ν
β
)
)
,
α
β
Doc 18
0.1597, -40.0000, 3.0000, 0.2785
testing/wikipedia/v3/14154.html
u
i
j
n
+
1
-
u
i
j
n
Δ
t
=
1
2
(
δ
x
2
+
δ
y
2
)
(
u
i
j
n
+
1
+
u
i
j
n
)
Doc 19
0.1593, -29.0000, 5.0000, 0.1593
testing/wikipedia/v3/21106.html
C
H
I
=
(
V
V
0
)
3
+
3
2
(
R
R
0
)
(
V
V
0
)
2
Doc 20
0.1524, -17.0000, 4.0000, 0.1524
testing/wikipedia/v3/21585.html
u
2
=
λ
2
+
1
r
2
(
p
2
2
m
-
1
2
m
g
z
)
.
Doc 22
0.1443, -18.0000, 4.0000, 0.1443
testing/wikipedia/v3/06836.html
R
d
=
r
d
2
+
3
4
(
m
e
m
d
)
2
(
λ
C
2
π
)
2
Doc 21
0.1443, -18.0000, 4.0000, 0.1443
testing/wikipedia/v3/25801.html
m
⩾
m
P
2
(
π
k
)
1
2
Doc 23
0.1348, -7.0000, 3.0000, 0.1348
testing/wikipedia/v3/26484.html
W
+
1
2
T
+
1
2
O
T
G
C
Doc 24
0.1348, -9.0000, 6.0000, 0.1348
testing/wikipedia/v3/10552.html
R
μ
´
α
ν
β
u
´
α
x
´
ν
u
´
β
=
-
f
´
μ
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
σ
t
=
8
π
3
(
α
λ
c
2
π
)
2
Doc 25
0.1348, -9.0000, 5.0000, 0.1348
testing/wikipedia/v3/05878.html
1
2
(
2
A
)
+
1
2
(
A
2
)
=
5
4
A
Doc 26
0.1348, -13.0000, 5.0000, 0.1348
testing/wikipedia/v3/10698.html
1
2
(
a
c
+
b
d
)
+
i
2
(
b
d
-
a
c
)
Doc 27
0.1348, -17.0000, 3.0000, 0.5488
testing/wikipedia/v3/27724.html
T
I
J
-
:=
1
2
(
T
I
J
+
i
2
ϵ
K
L
I
J
T
K
L
)
Doc 28
0.1348, -18.0000, 2.0000, 0.1348
testing/wikipedia/v3/29439.html
1
2
(
a
c
+
b
d
)
±
i
2
3
(
b
d
-
a
c
)
Doc 27
0.1348, -17.0000, 3.0000, 0.5488
testing/wikipedia/v3/27724.html
T
α
β
=
(
ρ
+
p
c
2
)
u
α
u
β
+
p
g
α
β
Doc 29
0.1261, -13.0000, 4.0000, 0.2109
testing/wikipedia/v3/01979.html
D
u
´
μ
D
τ
=
d
u
´
μ
d
τ
+
Γ
μ
α
β
u
´
α
u
´
β
=
0
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
(
p
+
r
2
)
(
q
+
s
2
)
Doc 30
0.1188, -6.0000, 4.0000, 0.1188
testing/wikipedia/v3/03760.html
(
p
-
1
2
)
(
q
-
1
2
)
,
Doc 31
0.1188, -7.0000, 4.0000, 0.1188
testing/wikipedia/v3/11626.html
ω
1
=
e
i
2
π
3
=
-
1
2
+
3
2
i
.
Doc 32
0.1188, -15.0000, 3.0000, 0.2117
testing/wikipedia/v3/03326.html
ω
=
-
1
3
ω
0
[
1
+
3
4
(
V
a
b
ℏ
ω
0
)
2
]
.
Doc 33
0.1188, -18.0000, 3.0000, 0.1188
testing/wikipedia/v3/23967.html
=
8
e
4
t
2
(
1
2
s
1
2
s
+
1
2
u
1
2
u
)
Doc 34
0.1188, -19.0000, 5.0000, 0.2376
testing/wikipedia/v3/14274.html
=
8
e
4
s
2
(
1
2
t
1
2
t
+
1
2
u
1
2
u
)
Doc 34
0.1188, -19.0000, 5.0000, 0.2376
testing/wikipedia/v3/14274.html
K
=
-
1
2
E
G
(
∂
∂
u
G
u
E
G
+
∂
∂
v
E
v
E
G
)
.
Doc 35
0.1188, -26.0000, 5.0000, 0.1188
testing/wikipedia/v3/03632.html
t
L
L
μ
ν
=
-
c
4
8
π
G
(
G
μ
ν
+
Λ
g
μ
ν
)
+
c
4
16
π
G
(
-
g
)
(
(
-
g
)
(
g
μ
ν
g
α
β
-
g
μ
α
g
ν
β
)
)
,
α
β
Doc 18
0.1597, -40.0000, 3.0000, 0.2785
testing/wikipedia/v3/14154.html
u
α
T
α
β
u
β
→
T
00
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
1
2
(
1
2
+
1
)
=
0.75
Doc 36
0.1099, -6.0000, 4.0000, 0.1099
testing/wikipedia/v3/12210.html
1
2
(
1
2
+
1
)
=
3
4
Doc 37
0.1099, -8.0000, 4.0000, 0.1099
testing/wikipedia/v3/13267.html
G
μ
ν
=
8
π
G
c
4
T
μ
ν
Doc 38
0.1099, -8.0000, 2.0000, 0.1099
testing/wikipedia/v3/27211.html
Doc 39
0.1099, -8.0000, 2.0000, 0.1099
testing/wikipedia/v3/10177.html
𝒢
α
β
=
8
π
G
c
4
T
´
α
β
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
1
2
(
3
2
)
6
E
1
=
-
77.5
e
V
Doc 40
0.1099, -10.0000, 4.0000, 0.1099
testing/wikipedia/v3/23263.html
Re
(
γ
)
≈
L
C
2
(
R
L
+
G
C
)
Doc 41
0.1099, -12.0000, 3.0000, 0.1099
testing/wikipedia/v3/01350.html
x
2
+
(
y
+
A
2
ψ
)
2
=
(
A
2
ψ
)
2
.
Doc 42
0.1099, -14.0000, 3.0000, 0.1099
testing/wikipedia/v3/01782.html
∇
2
A
=
-
μ
0
d
d
A
(
p
+
B
z
2
2
μ
0
)
Doc 43
0.1099, -16.0000, 4.0000, 0.1099
testing/wikipedia/v3/10539.html
w
n
=
sin
(
π
2
sin
2
[
π
2
N
(
n
+
1
2
)
]
)
Doc 44
0.1099, -16.0000, 3.0000, 0.1099
testing/wikipedia/v3/03200.html
P
m
o
v
e
l
e
f
t
=
1
2
+
1
2
(
x
c
+
|
x
|
)
Doc 45
0.1099, -19.0000, 3.0000, 0.1099
testing/wikipedia/v3/02839.html
=
-
-
2
α
(
2
π
)
d
/
2
(
d
2
)
!
(
1
2
F
)
d
/
2
,
Doc 46
0.1099, -21.0000, 4.0000, 0.1099
testing/wikipedia/v3/10974.html
|
x
-
1
2
(
a
c
+
b
d
)
|
=
1
2
(
b
d
-
a
c
)
Doc 27
0.1348, -17.0000, 3.0000, 0.5488
testing/wikipedia/v3/27724.html
1
2
(
a
c
+
b
d
)
-
3
i
2
3
(
b
d
-
a
c
)
Doc 27
0.1348, -17.0000, 3.0000, 0.5488
testing/wikipedia/v3/27724.html
S
=
n
R
ln
[
(
V
N
)
(
4
π
m
3
h
2
U
N
)
3
2
]
+
5
2
n
R
.
Doc 47
0.1099, -26.0000, 3.0000, 0.1099
testing/wikipedia/v3/09492.html
3
1
1
+
1
2
+
1
4
=
1
1
3
(
1
1
+
1
2
+
1
4
)
=
12
7
.
Doc 48
0.1099, -31.0000, 4.0000, 0.1099
testing/wikipedia/v3/00505.html
S
=
k
N
ln
[
(
V
N
)
(
U
N
)
3
2
]
+
3
2
k
N
(
5
3
+
ln
4
π
m
3
h
2
)
Doc 49
0.1099, -31.0000, 3.0000, 0.1099
testing/wikipedia/v3/08322.html
Doc 50
0.1099, -31.0000, 3.0000, 0.1099
testing/wikipedia/v3/03657.html
ψ
=
-
1
2
V
r
2
[
1
-
3
2
R
r
2
+
z
2
+
1
2
(
R
r
2
+
z
2
)
3
]
.
Doc 51
0.1099, -33.0000, 3.0000, 0.1099
testing/wikipedia/v3/02949.html
C
-
vertex
=
sec
2
(
A
2
)
:
sec
2
(
B
2
)
:
0
Doc 52
0.0992, -13.0000, 5.0000, 0.3841
testing/wikipedia/v3/02497.html
C
-
vertex
=
csc
2
(
A
2
)
:
csc
2
(
B
2
)
:
0
Doc 52
0.0992, -13.0000, 5.0000, 0.3841
testing/wikipedia/v3/02497.html
H
=
1
2
(
x
p
+
p
x
)
=
-
i
(
x
d
d
x
+
1
2
)
.
Doc 53
0.0992, -19.0000, 4.0000, 0.0992
testing/wikipedia/v3/05993.html
(
ρ
0
+
ρ
0
s
)
(
∂
∂
t
+
u
∂
∂
x
)
u
+
∂
∂
x
(
P
0
+
p
)
=
0
Doc 54
0.0992, -25.0000, 5.0000, 0.0992
testing/wikipedia/v3/10839.html
ζ
=
-
1
2
+
3
2
i
Doc 32
0.1188, -15.0000, 3.0000, 0.2117
testing/wikipedia/v3/03326.html
h
α
β
=
g
α
β
-
u
α
u
β
Doc 55
0.0929, -7.0000, 2.0000, 0.0929
testing/wikipedia/v3/11236.html
ω
2
=
-
1
2
+
3
2
i
Doc 56
0.0929, -8.0000, 3.0000, 0.0929
testing/wikipedia/v3/17084.html
sec
2
(
A
2
)
:
sec
2
(
B
2
)
:
sec
2
(
C
2
)
Doc 52
0.0992, -13.0000, 5.0000, 0.3841
testing/wikipedia/v3/02497.html
csc
2
(
A
2
)
:
csc
2
(
B
2
)
:
csc
2
(
C
2
)
Doc 52
0.0992, -13.0000, 5.0000, 0.3841
testing/wikipedia/v3/02497.html
T
α
S
α
=
T
α
η
α
β
S
β
=
T
α
η
α
β
S
β
=
invariant scalar
Doc 57
0.0929, -17.0000, 5.0000, 0.0929
testing/wikipedia/v3/00927.html
=
1
2
(
1
-
1
2
+
1
3
+
⋯
)
=
1
2
ln
(
2
)
Doc 58
0.0929, -18.0000, 4.0000, 0.0929
testing/wikipedia/v3/09544.html
a
˙
2
2
-
G
4
π
a
3
3
ρ
a
=
-
k
c
2
2
.
Doc 59
0.0929, -18.0000, 3.0000, 0.0929
testing/wikipedia/v3/04142.html
y
(
t
)
=
(
C
+
m
(
t
)
)
(
1
2
+
1
2
cos
(
2
ω
t
)
)
.
Doc 60
0.0929, -19.0000, 2.0000, 0.0929
testing/wikipedia/v3/04161.html
ε
α
β
=
1
2
(
u
α
,
β
+
u
β
,
α
)
-
x
3
w
,
α
β
.
Doc 61
0.0929, -20.0000, 4.0000, 0.0929
testing/wikipedia/v3/26535.html
Doc 62
0.0929, -20.0000, 4.0000, 0.0929
testing/wikipedia/v3/25749.html
T
≡
T
α
α
=
-
u
α
u
α
T
=
-
u
α
T
η
α
β
u
β
→
-
T
00
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
T
´
α
β
=
1
-
g
(
d
d
x
ν
∂
ℒ
e
∂
(
d
g
α
β
d
x
ν
)
-
∂
ℒ
e
∂
g
α
β
)
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
C
=
(
8
π
G
c
4
)
-
1
Doc 1
1.0000, 0.0000, 41.0000, 5.4193
testing/wikipedia/v3/12471.html
g
α
β
u
α
u
β
=
-
c
2
Doc 63
0.0848, -7.0000, 2.0000, 0.0848
testing/wikipedia/v3/00566.html
P
+
=
1
2
(
I
+
A
α
)
Doc 64
0.0848, -8.0000, 2.0000, 0.0848
testing/wikipedia/v3/05345.html
u
α
u
β
g
α
β
=
-
c
2
.
Doc 29
0.1261, -13.0000, 4.0000, 0.2109
testing/wikipedia/v3/01979.html
C
2
=
T
2
+
1
2
(
T
1
)
2
Doc 65
0.0848, -9.0000, 4.0000, 0.0848
testing/wikipedia/v3/04776.html
x
n
=
-
cos
(
π
N
(
n
+
1
2
)
)
Doc 66
0.0848, -11.0000, 3.0000, 0.0848
testing/wikipedia/v3/27459.html
S
(
T
)
=
C
exp
(
A
T
2
+
B
2
T
)
-
1
Doc 67
0.0848, -15.0000, 4.0000, 0.0848
testing/wikipedia/v3/25555.html
∂
t
u
+
∂
x
[
u
2
2
+
G
2
*
(
b
u
2
2
+
(
3
-
b
)
u
x
2
2
)
]
=
0.
Doc 68
0.0848, -30.0000, 3.0000, 0.0848
testing/wikipedia/v3/22036.html
ψ
(
1
3
)
=
-
π
2
3
-
3
2
ln
3
-
γ
Doc 69
0.0709, -15.0000, 3.0000, 0.0709
testing/wikipedia/v3/04624.html
F
=
-
G
M
m
r
2
(
1
+
(
2
+
2
γ
-
β
)
(
h
r
c
)
2
)
Doc 3
0.2198, -38.0000, 5.0000, 0.2859
testing/wikipedia/v3/25303.html
p
(
1
2
)
=
-
8
Doc 27
0.1348, -17.0000, 3.0000, 0.5488
testing/wikipedia/v3/27724.html
=
(
1
2
+
1
3
)
Doc 70
0.0594, -6.0000, 3.0000, 0.0594
testing/wikipedia/v3/12587.html
=
1
3
⋅
(
1
2
0
+
1
2
1
+
1
2
2
)
Doc 71
0.0594, -17.0000, 3.0000, 0.1188
testing/wikipedia/v3/06512.html
1
3
×
(
2
3
+
1
3
+
1
2
)
=
1
2
Doc 72
0.0594, -17.0000, 3.0000, 0.0594
testing/wikipedia/v3/13309.html
(
1
2
(
x
-
1
x
)
)
2
+
1
=
(
1
2
(
x
+
1
x
)
)
2
,
Doc 73
0.0594, -23.0000, 3.0000, 0.0594
testing/wikipedia/v3/00703.html
=
1
3
⋅
(
1
2
1
-
1
+
1
2
2
-
1
+
1
2
3
-
1
)
Doc 71
0.0594, -17.0000, 3.0000, 0.1188
testing/wikipedia/v3/06512.html