tangent
Not Supported
*1*
=
∫
0
∞
*2*
2
*3*
d
*1*
∫
0
∞
*3*
d
*1*
Search
Returned 77 matches (100 formulae, 90 docs)
Lookup 191.089 ms, Re-ranking 0.125 ms
Found 619909 tuple postings, 183019 formulae, 22250 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
Doc 1
0.5532
0.8470
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Delay_spread.html
τ
rms
=
∫
0
∞
(
τ
-
τ
¯
)
2
A
c
(
τ
)
d
τ
∫
0
∞
A
c
(
τ
)
d
τ
τ
¯
=
∫
0
∞
τ
A
c
(
τ
)
d
τ
∫
0
∞
A
c
(
τ
)
d
τ
Doc 2
0.4706
0.4706
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Luminous_efficacy.html
∫
0
∞
y
λ
J
λ
d
λ
∫
0
∞
J
λ
d
λ
,
Doc 3
0.4300
0.8014
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/AB_magnitude.html
λ
piv
=
∫
e
(
λ
)
d
λ
∫
e
(
λ
)
λ
-
2
d
λ
λ
piv
=
∫
e
(
λ
)
λ
d
λ
∫
e
(
λ
)
λ
-
1
d
λ
Doc 4
0.3562
0.3562
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Fresnel_zone.html
F
n
=
n
λ
d
1
d
2
d
1
+
d
2
Doc 5
0.3363
0.3363
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Equations_for_a_falling_body.html
v
i
=
2
G
M
d
r
2
Doc 6
0.3238
0.5638
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Plasma_fusion_preface.html
v
=
k
e
2
m
r
v
=
2
k
T
m
Doc 7
0.3063
0.3063
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Free_electron_model.html
ω
p
=
n
e
2
ϵ
0
m
Doc 8
0.3063
0.3063
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Quartic_interaction.html
v
=
2
μ
0
2
3
λ
Doc 9
0.2979
0.2979
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Twin-lead.html
Z
=
R
+
j
ω
L
G
+
j
ω
C
Doc 10
0.2958
0.2958
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Heaviside_condition.html
Z
0
=
R
+
j
ω
L
G
+
j
ω
C
Doc 11
0.2958
0.2958
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Characteristic_admittance.html
Y
0
=
G
+
j
ω
C
R
+
j
ω
L
Doc 12
0.2958
0.2958
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Characteristic_impedance.html
Z
0
=
R
+
j
ω
L
G
+
j
ω
C
Doc 13
0.2957
0.2957
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Spinodal_decomposition.html
λ
c
=
8
π
2
κ
f
′′
.
Doc 14
0.2906
0.2906
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Surface_plasmon_polariton.html
ω
P
=
n
e
2
ε
0
m
*
Doc 15
0.2897
0.2897
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Transmission_line.html
Z
0
=
R
+
j
ω
L
G
+
j
ω
C
.
Doc 16
0.2885
0.5688
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Logan_plot.html
∫
0
t
ROI
(
τ
)
d
τ
ROI
(
t
)
∫
0
t
C
p
(
τ
)
d
τ
ROI
(
t
)
Doc 17
0.2880
0.5466
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Pulse_wave_velocity.html
PWV
=
d
P
⋅
V
ρ
⋅
d
V
PWV
=
E
inc
⋅
h
2
r
ρ
Doc 18
0.2857
0.2857
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Rüchardt_experiment.html
ω
=
γ
P
A
2
m
V
Doc 19
0.2857
0.2857
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Material_failure_theory.html
σ
=
2
E
γ
π
a
Doc 20
0.2857
0.2857
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Wave_impedance.html
Z
=
j
ω
μ
σ
+
j
ω
ε
Doc 21
0.2857
0.2857
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Self-focusing.html
ω
p
=
n
e
2
γ
m
ϵ
0
Doc 22
0.2857
0.2857
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Newton's_theorem_of_revolving_orbits.html
k
=
a
+
b
a
m
+
b
n
Doc 23
0.2857
0.2857
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Incircle_and_excircles_of_a_triangle.html
r
=
x
y
z
x
+
y
+
z
Doc 24
0.2830
0.2830
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Spin-exchange_interaction.html
v
¯
=
8
R
T
π
m
Doc 25
0.2830
0.2830
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Langmuir_(unit).html
u
¯
=
8
k
T
π
m
Doc 26
0.2787
0.5574
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Coronal_seismology.html
ω
S
=
k
z
2
B
2
μ
ρ
e
ω
A
=
k
z
2
B
2
μ
ρ
i
Doc 27
0.2759
0.2759
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Cant_(road::rail).html
v
m
a
x
=
E
a
+
3
0.00066
d
Doc 28
0.2759
0.2759
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Rail_speed_limits_in_the_United_States.html
V
m
a
x
=
E
a
+
3
0.0007
d
Doc 29
0.2752
0.2752
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Redescending_M-estimator.html
∫
Ψ
2
d
F
(
∫
Ψ
′
d
F
)
2
Doc 30
0.2745
0.2745
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Pound–Rebka_experiment.html
f
r
=
1
-
v
/
c
1
+
v
/
c
f
e
.
Doc 31
0.2720
0.2720
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Electric-field_screening.html
k
0
=
def
ρ
e
2
ϵ
0
k
B
T
Doc 32
0.2707
0.2707
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/James_Hopwood_Jeans.html
λ
J
=
15
k
B
T
4
π
G
m
ρ
Doc 33
0.2703
0.5334
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Standard_error.html
FPC
=
N
-
n
N
-
1
f
=
1
+
ρ
1
-
ρ
,
Doc 34
0.2703
0.2703
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Quasicircle.html
K
=
1
+
t
1
-
t
Doc 35
0.2679
0.2679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Knudsen_number.html
c
¯
=
8
k
B
T
π
m
Doc 36
0.2679
0.2679
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Elastic_collision.html
e
s
=
c
+
v
c
-
v
Doc 37
0.2667
0.2667
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Kirchhoff's_law_of_thermal_radiation.html
α
sun
=
∫
0
∞
α
λ
I
λ
sun
(
λ
)
d
λ
∫
0
∞
I
λ
sun
(
λ
)
d
λ
Doc 38
0.2647
0.2647
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Jeans_instability.html
λ
J
=
15
k
B
T
4
π
G
μ
ρ
,
Doc 39
0.2639
0.2639
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Poisson–Boltzmann_equation.html
K
=
2
c
0
e
2
ϵ
ϵ
0
k
B
T
Doc 40
0.2632
0.5263
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Thermal_velocity.html
v
t
h
=
2
k
B
T
π
m
v
t
h
=
8
k
B
T
m
π
Doc 41
0.2632
0.2632
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Margin_of_error.html
FPC
=
N
-
n
N
-
1
.
Doc 42
0.2623
0.2623
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Lindhard_theory.html
κ
=
4
π
e
2
n
β
ϵ
Doc 43
0.2623
0.2623
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Limb_darkening.html
I
m
=
∫
I
(
ψ
)
d
ω
∫
d
ω
Doc 44
0.2609
0.2609
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Circumscribed_circle.html
diameter
=
2
⋅
area
sin
A
sin
B
sin
C
.
Doc 45
0.2609
0.2609
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Economic_order_quantity.html
=
2
*
10000
*
2
8
*
0.02
Doc 46
0.2609
0.2609
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Economic_batch_quantity.html
Economic batch quantity
=
2
⋅
annual demand
⋅
setup costs
inventory carrying cost per unit
Doc 47
0.2602
0.2602
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Debye_length.html
L
D
=
ε
k
B
T
q
2
N
d
Doc 48
0.2599
0.2599
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Self-healing_hydrogels.html
κ
=
Σ
(
z
*
e
)
2
C
0
*
ϵ
r
ϵ
0
k
B
T
Doc 49
0.2586
0.2586
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Template:V2::doc.html
v
2
=
2
×
G
×
M
R
Doc 50
0.2569
0.2569
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Flight_dynamics_(fixed-wing_aircraft).html
2
π
T
=
2
g
2
U
2
Doc 51
0.2564
0.5106
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Relativistic_Doppler_effect.html
f
s
f
o
=
1
+
β
1
-
β
z
=
1
+
β
1
-
β
-
1.
Doc 52
0.2550
0.2550
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Doppler_broadening.html
Δ
f
FWHM
=
8
k
T
ln
2
m
c
2
f
0
Doc 53
0.2545
0.2545
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/No-three-in-line_problem.html
c
=
2
π
2
3
3
≈
1.874.
Doc 54
0.2542
0.7606
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Terminal_velocity.html
v
=
2
m
g
ρ
A
C
d
v
=
2
m
g
ρ
A
C
d
V
t
=
2
m
g
ρ
A
C
d
Doc 55
0.2542
0.2542
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Draft:Template:convert::kps::z::doc.html
z
=
c
+
v
c
-
v
-
1
Doc 56
0.2542
0.2542
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Draft:Template:calculate::z=√((c+v)÷(c-v))-1::doc.html
z
=
c
+
v
c
-
v
-
1
Doc 57
0.2542
0.2542
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Collision_theory.html
c
A
=
8
k
B
T
π
m
A
Doc 58
0.2540
0.2540
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Bohr_model.html
v
=
Z
k
e
e
2
m
e
r
.
Doc 59
0.2540
0.2540
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Particle_size.html
D
=
2
3
W
4
π
d
g
3
Doc 60
0.2540
0.2540
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Corona.html
λ
D
=
k
B
T
4
π
n
e
2
Doc 61
0.2540
0.2540
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Assumed_mean.html
σ
=
B
-
N
D
2
N
-
1
Doc 62
0.2540
0.2540
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Nanofluidics.html
κ
=
8
π
n
e
2
ϵ
k
T
Doc 63
0.2521
0.2521
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Speed_skydiving.html
v
t
=
2
m
g
ρ
A
C
d
Doc 64
0.2519
0.2519
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Impedance_matching.html
X
1
=
R
2
R
1
2
R
1
-
R
2
Doc 65
0.2517
0.2517
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Modified_internal_rate_of_return.html
MIRR
=
F
V
(
positive cash flows, reinvestment rate
)
-
P
V
(
negative cash flows, finance rate
)
n
-
1
Doc 66
0.2500
0.2500
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Weight_function.html
∫
Ω
f
(
x
)
w
(
x
)
d
x
∫
Ω
w
(
x
)
d
x
Doc 67
0.2481
0.2481
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Coulomb_collision.html
λ
D
=
ϵ
0
k
T
e
n
e
e
2
Doc 68
0.2479
0.2479
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Free_fall.html
v
∞
=
2
m
g
ρ
C
D
A
.
Doc 69
0.2476
0.2476
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Hadamard's_dynamical_system.html
λ
=
2
E
m
R
2
Doc 70
0.2476
0.2476
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Semicircular_potential_well.html
m
=
2
I
E
ℏ
2
Doc 71
0.2472
0.2472
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Radio_frequency_microelectromechanical_system.html
R
=
λ
2
EIRP
G
R
/
T
σ
64
π
3
k
B
BW
SNR
4
Doc 72
0.2471
0.2471
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Redshift.html
1
+
z
=
1
+
v
/
c
1
-
v
/
c
Doc 73
0.2459
0.2459
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Drag_(physics).html
v
t
=
2
m
g
ρ
A
C
d
.
Doc 74
0.2459
0.2459
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Fracture.html
σ
fracture
=
E
γ
ρ
4
a
r
o
.
Doc 75
0.2454
0.2454
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Cevian.html
d
=
2
b
2
+
2
c
2
-
a
2
4
.
Doc 76
0.2443
0.2443
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Ring_laser.html
σ
=
h
f
0
3
2
P
Q
2
T
Doc 77
0.2441
0.2441
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Opacity_(optics).html
1
κ
=
∫
0
∞
κ
ν
-
1
u
(
ν
,
T
)
d
ν
∫
0
∞
u
(
ν
,
T
)
d
ν
Doc 78
0.2439
0.7317
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Median_(geometry).html
m
c
=
2
a
2
+
2
b
2
-
c
2
4
,
m
b
=
2
a
2
+
2
c
2
-
b
2
4
,
m
a
=
2
b
2
+
2
c
2
-
a
2
4
,
Doc 79
0.2424
0.2424
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Planck_particle.html
m
=
h
c
2
G
Doc 80
0.2424
0.2424
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Soap_film.html
V
=
2
γ
ρ
h
Doc 81
0.2424
0.2424
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Orbital_period.html
T
=
3
π
G
ρ
Doc 82
0.2416
0.2416
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Centroid.html
C
=
∫
x
g
(
x
)
d
x
∫
g
(
x
)
d
x
Doc 83
0.2406
0.2406
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Black_hole_electron.html
r
q
=
q
2
G
4
π
ϵ
0
c
4
Doc 84
0.2400
0.2400
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Fracture_mechanics.html
C
=
2
E
γ
π
Doc 85
0.2400
0.2400
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Peeler_centrifuge.html
δ
=
μ
/
ρ
Ω
Doc 86
0.2400
0.2400
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Boundary_layer.html
δ
2
=
μ
L
ρ
v
Doc 87
0.2400
0.2400
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Electrical_mobility.html
v
=
3
k
T
m
Doc 88
0.2400
0.2400
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Dynamic_similarity_(Reynolds_and_Womersley_numbers).html
δ
2
=
μ
L
ρ
V
Doc 89
0.2400
0.2400
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/List_of_equations_in_gravitation.html
v
=
2
G
M
r
Doc 90
0.2400
0.2400
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Laughlin_wavefunction.html
l
B
=
ℏ
c
e
B