Returned 99 matches (100 formulae, 80 docs)
    Lookup 402.595 ms, Re-ranking 1300.585 ms
    Found 1101455 tuple postings, 181570 formulae, 22149 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
1.0000
0.0000
8.0000
1.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Hyperbolic_law_of_cosines.html
cos α = - cos β cos γ + sin β sin γ cosh a k ,

Doc 2
0.5106
-5.0000
4.0000
1.0213
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Riemann's_differential_equation.html
α + α + β + β + γ + γ = 1.
α + α + β + β + γ + γ = 1.

Doc 3
0.4348
-2.0000
2.0000
0.7654
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Inverse_Galois_problem.html
α β + β γ + γ α = 2
α + β + γ = 1

Doc 4
0.4348
-5.0000
2.0000
0.4348
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Quantum_group.html
α α * + μ 2 β * β = α * α + β * β = I ,

Doc 5
0.4348
-6.0000
3.0000
0.4348
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Baker's_theorem.html
Λ = β 0 + β 1 λ 1 + + β n λ n

Doc 6
0.4054
-5.0000
1.0000
0.4054
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Heun_function.html
ϵ = α + β - γ - δ + 1

Doc 7
0.4054
-12.0000
1.0000
0.4054
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Roll's_critique.html
E ( R i ) = α + β 1 F 1 + + β N F N .

Doc 8
0.3810
-3.0000
3.0000
0.7115
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Surface_tension.html
d F = - P d V + γ d A
γ ls - γ sa = - γ la cos θ

Doc 9
0.3810
-3.0000
3.0000
0.3810
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Lotka–Volterra_equation.html
V = - δ x + γ ln ( x ) - β y + α ln ( y ) .

Doc 10
0.3810
-4.0000
2.0000
0.7115
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/BKL_singularity.html
χ = α - β = k ln ξ + const ,
1 2 ( α + β + γ ) τ τ = α τ β τ + α τ γ τ + β τ γ τ .

Doc 11
0.3810
-6.0000
3.0000
0.7115
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Differential_geometry_of_surfaces.html
Δ K d A = α + β + γ - π .
= α + β + γ - π ,

Doc 12
0.3810
-8.0000
4.0000
0.3810
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Helmholtz_free_energy.html
d ( log Z ) = - d ( β U ) + β d U + β X d x

Doc 13
0.3810
-9.0000
2.0000
1.4022
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Proofs_of_trigonometric_identities.html
cos ( α - β ) = cos α cos - β - sin α sin - β
sin ( α + β ) = sin α cos β + cos α sin β
sin ( α - β ) = sin α cos - β + cos α sin - β
cos ( α - β ) = cos α cos β + sin α sin β
cos ( α - β ) = cos α cos β + sin α sin β

Doc 14
0.3810
-10.0000
2.0000
0.3810
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Propagation_constant.html
γ T o t = γ 1 + γ 2 + γ 3 + + γ n

Doc 15
0.3582
-1.0000
4.0000
0.6135
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Ordinal_arithmetic.html
α < β γ + α < γ + β
α < β α + γ β + γ

Doc 16
0.3582
-2.0000
3.0000
0.6135
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Triangle_inequality.html
α = π / 2 - γ , while β = π / 2 - γ / 2 ,
2 β + γ = π .

Doc 17
0.3582
-4.0000
1.0000
0.3582
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Ecological_fallacy.html
Y i = α + β X i + u i ,

Doc 18
0.3582
-8.0000
2.0000
0.9190
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Gamma_matrices.html
= 2 γ ρ γ ν - γ ν 2 η μ ρ γ μ + 4 γ ν γ ρ
= 2 γ ρ γ ν - 2 γ ν γ ρ + 4 γ ν γ ρ
= 2 γ ν - 4 γ ν = - 2 γ ν .
Doc 19
0.3306
0.0000
3.0000
0.5859
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Chevalley_basis.html
β + α γ + α
β 0 + γ 0 = β + γ

Doc 20
0.3306
0.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Geometry_index.html
τ 5 = β - α 60 - 0.01667 α + 0.01667 β

Doc 21
0.3306
0.0000
1.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Bhargava_cube.html
x α x + β y , y γ x + δ y

Doc 22
0.3306
-1.0000
2.0000
1.2219
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Law_of_cosines.html
α + β + γ = 180.
sin ( α + γ ) = sin α cos γ + sin γ cos α
b 2 = b c cos α + a b cos γ .
a 2 = a c cos β + a b cos γ ,

Doc 23
0.3306
-1.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Circumconic_and_inconic.html
α = β = γ = 1 / 3.

Doc 24
0.3306
-1.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Homogeneous_differential_equation.html
t = x + α ; z = y + β .

Doc 25
0.3306
-1.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Solution_of_triangles.html
α + β + γ = 180

Doc 26
0.3306
-1.0000
1.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Normal_variance-mean_mixture.html
Y = α + β V + σ V X ,

Doc 27
0.3306
-2.0000
1.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Recurrence_relation.html
λ 1 λ 2 = α 2 + β 2 = - B ,

Doc 28
0.3306
-3.0000
3.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Pole–zero_plot.html
s = α 1 = - 3 + 4 j

Doc 29
0.3306
-4.0000
3.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Duffin–Kemmer–Petiau_algebra.html
β a γ + γ β a = β a

Doc 30
0.3306
-4.0000
2.0000
0.6110
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Rushbrooke_inequality.html
α , α , β , γ , γ
α + 2 β + γ 2.

Doc 31
0.3306
-4.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Plasma_fusion_preface.html
r 1 , 2 = - b + / - j γ

Doc 32
0.3306
-4.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Magnetic_anisotropy.html
α 2 + β 2 + γ 2 = 1

Doc 33
0.3306
-4.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Widom_scaling.html
α , α , β , γ , γ

Doc 34
0.3306
-5.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Douady_rabbit.html
γ = 2 - γ D = - .55268 + .959456 i

Doc 35
0.3306
-5.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Ordinal_collapsing_function.html
α = δ β 1 γ 1 + + δ β k γ k

Doc 36
0.3306
-5.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Brocard_points.html
cot ω = cot α + cot β + cot γ .

Doc 37
0.3306
-9.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Bose–Hubbard_model.html
i = j = k = l , α = β = γ = δ = 0

Doc 38
0.3306
-13.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Motor_variable.html
w = α z + β γ z + δ where α , β , γ , δ

Doc 39
0.3306
-15.0000
2.0000
0.3306
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Triangle.html
r R = 4 T 2 s a b c = cos α + cos β + cos γ - 1 ;

Doc 40
0.3158
-3.0000
4.0000
0.3158
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Riemannian_connection_on_a_surface.html
d α = β γ , d β = γ α , d γ = α β .

Doc 41
0.3158
-4.0000
1.0000
0.3158
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Cyclic_quadrilateral.html
α + γ = β + δ = π = 180 .

Doc 42
0.3158
-8.0000
2.0000
1.1319
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/List_of_relativistic_equations.html
γ v t = γ 2 v t - γ 2 x + x
c t = γ c t - γ β x
γ v t = γ 2 v t - γ 2 β 2 x
x = γ x - γ β c t

Doc 43
0.3000
-2.0000
2.0000
0.3000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Constant_k_filter.html
γ = α + i β = 0 + i sin - 1 ω ω c

Doc 44
0.3000
-2.0000
1.0000
0.3000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Student's_t-test.html
Y = α + β x + ε ,

Doc 45
0.3000
-4.0000
3.0000
0.5151
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Universal_joint.html
tan γ 2 = cos β tan γ 1 tan γ 4 = cos β tan γ 3
tan γ 1 = cos β tan γ 2

Doc 46
0.3000
-4.0000
2.0000
0.6000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Ordinary_least_squares.html
y = X 1 β 1 + X 2 β 2 + ε ,
y i = α + β x i + ε i .

Doc 47
0.3000
-4.0000
1.0000
0.3000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Prediction_interval.html
y d = α + β x d + ϵ d .

Doc 48
0.3000
-4.0000
1.0000
0.3000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Simple_linear_regression.html
y i = α + β x i + ε i .

Doc 49
0.3000
-5.0000
3.0000
0.3000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Binomial_approximation.html
= 1 - α x γ + ( 1 / 2 ) ( α x ) 2 ( γ + 1 ) γ -

Doc 50
0.3000
-5.0000
3.0000
0.3000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Solow_residual.html
y = C + β k + γ + ε .

Doc 51
0.3000
-7.0000
3.0000
0.3000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Endogeneity_(econometrics).html
y i = α + β x i + γ z i + u i

Doc 52
0.3000
-7.0000
2.0000
0.3000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Comma_category.html
α = β , α = β , g = h

Doc 53
0.3000
-9.0000
3.0000
0.3000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Adomian_decomposition_method.html
u = α + β x + γ x 2 / 2 - L - 1 N u

Doc 54
0.2804
-3.0000
2.0000
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Boundary-incompressible_surface.html
α β = α = β

Doc 55
0.2804
-3.0000
1.0000
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Window_function.html
α = 0.54 , β = 1 - α = 0.46 ,

Doc 56
0.2804
-5.0000
3.0000
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Darlington_transistor.html
β Darlington = β 1 β 2 + β 1 + β 2

Doc 57
0.2804
-5.0000
2.0000
1.0714
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Rotation_group_SO(3).html
Z = α X + β Y + γ [ X , Y ] ,
Z = α X + β Y + γ [ X , Y ] ,
ζ = α ζ + β γ ζ + δ , α δ - β γ 0.
( α β γ δ ) , α δ - β γ = 1 ,

Doc 58
0.2804
-5.0000
2.0000
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Rotation_matrix.html
Z = α X + β Y + γ [ X , Y ] ,

Doc 59
0.2804
-5.0000
2.0000
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Prisoner's_dilemma.html
α s x + β s y + γ = 0

Doc 60
0.2804
-6.0000
2.0000
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Hurwitz_zeta_function.html
γ 0 ( 1 ) = - ψ ( 1 ) = γ 0 = γ

Doc 61
0.2804
-6.0000
2.0000
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Convex_conjugate.html
g ( x ) = α + β x + γ f ( λ x + δ )

Doc 62
0.2804
-7.0000
3.0000
0.7910
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Parameterized_post-Newtonian_formalism.html
ζ 2 = 2 β + 2 β 2 - 3 γ - 1
α 1 = 7 Δ 1 + Δ 2 - 4 γ - 4
α 3 = 4 β 1 - 2 γ - 2 - ζ
Doc 63
0.2804
-8.0000
3.0000
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Wetting.html
γ α θ cos α + γ θ β cos β + γ α β = 0

Doc 64
0.2804
-8.0000
3.0000
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Ideal_surface.html
γ α θ cos α + γ θ β cos β + γ α β = 0

Doc 65
0.2804
-8.0000
2.0000
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Circumscribed_circle.html
P c = α P 1 + β P 2 + γ P 3

Doc 66
0.2804
-8.0000
2.0000
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Choice_model_simulation.html
U i = α P i + β D i + γ Y + ε i

Doc 67
0.2804
-10.0000
2.0000
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Two-way_analysis_of_variance.html
μ i j = μ + α i + β j + γ i j

Doc 68
0.2553
0.0000
1.0000
0.2553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Apollonian_circles.html
α ( x 2 + y 2 ) - 2 β x - 2 γ y + δ = 0 ,

Doc 69
0.2553
0.0000
1.0000
0.2553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Polynomial_least_squares.html
z = y + ε = α + β t + ε

Doc 70
0.2553
0.0000
1.0000
0.2553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Differential_form.html
α ( β + γ ) = α β + α γ .

Doc 71
0.2553
0.0000
0.0000
0.2553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Weighted_constraint_satisfaction_problem.html
α β = α - β

Doc 72
0.2553
-1.0000
1.0000
0.2553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Qutrit.html
| ψ = α | 0 + β | 1 + γ | 2

Doc 73
0.2553
-1.0000
1.0000
0.2553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/KPP-type_equation.html
u t - α u - β u 2 + γ u 3 = 0

Doc 74
0.2553
-2.0000
2.0000
0.2553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Modulational_instability.html
β 2 2 ω m 2 + 2 γ P β 2 < 0

Doc 75
0.2553
-6.0000
1.0000
0.2553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Epidemic_model.html
d S d T = B - β S I - μ S + γ I

Doc 76
0.2553
-6.0000
0.0000
0.2553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/List_of_trigonometric_identities.html
sin ( α + β ) = sin α cos β + cos α sin β

Doc 77
0.2553
-6.0000
0.0000
0.2553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Machin-like_formula.html
sin ( α + β ) = sin α cos β + cos α sin β

Doc 78
0.2553
-7.0000
0.0000
0.2553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Berry_connection_and_curvature.html
γ ~ n ( t ) = γ n ( t ) + β ( t ) - β ( 0 )

Doc 79
0.2553
-8.0000
1.0000
0.2553
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Quantum_spacetime.html
det q ( α β γ δ ) = α δ - q 2 γ β

Doc 80
0.2151
-2.0000
3.0000
0.2151
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/De_Rham_cohomology.html
ω = d α + δ β + γ