tangent
Not Supported
L
(
*1*
,
*2*
,
*3*
)
=
∑
*4*
=
0
∞
exp
(
2
π
i
*1*
*4*
)
(
*4*
+
*2*
)
*3*
Search
Returned 94 matches (100 formulae, 81 docs)
Lookup 434.350 ms, Re-ranking 2885.004 ms
Found 1285716 tuple postings, 226251 formulae, 23811 documents
[ formulas ]
[ documents ]
[ documents-by-formula ]
L
(
λ
,
α
,
s
)
=
∑
n
=
0
∞
exp
(
2
π
i
λ
n
)
(
n
+
α
)
s
.
Doc 1
1.0000, -1.0000, 17.0000, 2.5376
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lerch_zeta_function.html
Φ
(
z
,
s
,
q
)
=
∑
k
=
0
∞
z
k
(
k
+
q
)
s
Doc 2
0.6651, -3.0000, 11.0000, 1.3120
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Riemann_zeta_function.html
Doc 3
0.6651, -3.0000, 11.0000, 1.2121
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Hurwitz_zeta_function.html
Φ
(
z
,
s
,
α
)
=
∑
n
=
0
∞
z
n
(
n
+
α
)
s
.
Doc 1
1.0000, -1.0000, 17.0000, 2.5376
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lerch_zeta_function.html
Doc 4
0.6651, -4.0000, 11.0000, 0.6651
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Catalan's_constant.html
ζ
(
s
,
q
)
=
∑
k
=
0
∞
1
(
k
+
q
)
s
Doc 2
0.6651, -3.0000, 11.0000, 1.3120
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Riemann_zeta_function.html
ζ
(
s
,
a
)
=
∑
n
=
0
∞
1
(
n
+
a
)
s
Doc 5
0.6468, -1.0000, 9.0000, 0.6468
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Ramanujan's_master_theorem.html
ζ
(
s
,
t
)
=
∑
n
=
1
∞
H
n
,
t
(
n
+
1
)
s
Doc 6
0.6468, -4.0000, 8.0000, 1.0974
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Multiple_zeta_function.html
S
ν
(
x
)
=
∑
k
=
0
∞
sin
(
(
2
k
+
1
)
π
x
)
(
2
k
+
1
)
ν
Doc 7
0.6429, -7.0000, 10.0000, 0.6429
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_polynomials.html
Z
(
P
,
Q
,
s
)
=
∑
n
=
1
∞
f
n
(
P
)
f
n
(
Q
)
λ
n
s
Doc 8
0.6258, -8.0000, 9.0000, 0.6258
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Minakshisundaram–Pleijel_zeta_function.html
NPV
(
i
,
N
)
=
∑
t
=
0
N
R
t
(
1
+
i
)
t
Doc 9
0.5864, -3.0000, 8.0000, 1.1334
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Net_present_value.html
Φ
(
z
,
s
,
a
)
=
z
n
Φ
(
z
,
s
,
a
+
n
)
+
∑
k
=
0
n
-
1
z
k
(
k
+
a
)
s
Doc 1
1.0000, -1.0000, 17.0000, 2.5376
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lerch_zeta_function.html
L
(
s
,
χ
)
=
∑
n
=
1
∞
χ
(
n
)
n
s
Doc 12
0.5470, -2.0000, 8.0000, 0.5470
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Dirichlet_character.html
L
(
χ
,
s
)
=
∑
n
=
1
∞
χ
(
n
)
n
s
Doc 11
0.5470, -2.0000, 8.0000, 0.5470
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Generalized_Riemann_hypothesis.html
f
(
x
)
=
∑
n
=
0
∞
s
(
2
n
x
)
2
n
Doc 10
0.5470, -2.0000, 8.0000, 1.0462
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Draft:List_of_shape_topics_in_various_fields.html
NPV
(
i
)
=
∑
t
=
0
N
R
t
(
1
+
i
)
t
Doc 9
0.5864, -3.0000, 8.0000, 1.1334
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Net_present_value.html
blanc
(
x
)
=
∑
n
=
0
∞
s
(
2
n
x
)
2
n
,
Doc 15
0.5470, -3.0000, 8.0000, 0.5470
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Blancmange_curve.html
L
(
s
,
χ
)
=
∑
n
=
1
∞
χ
(
n
)
n
s
.
Doc 13
0.5470, -3.0000, 8.0000, 0.8008
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_L-function.html
Z
(
λ
,
ν
)
=
∑
j
=
0
∞
λ
j
(
j
!
)
ν
.
Doc 14
0.5470, -3.0000, 8.0000, 0.5470
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Conway–Maxwell–Poisson_distribution.html
ζ
(
s
,
q
)
=
∑
n
=
0
∞
1
(
q
+
n
)
s
.
Doc 3
0.6651, -3.0000, 11.0000, 1.2121
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Hurwitz_zeta_function.html
χ
ν
(
z
)
=
∑
k
=
0
∞
z
2
k
+
1
(
2
k
+
1
)
ν
.
Doc 16
0.5470, -7.0000, 8.0000, 0.5470
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Legendre_chi_function.html
ω
(
z
)
=
∑
n
=
0
+
∞
q
n
(
ω
a
)
(
1
+
ω
a
)
2
n
-
1
(
z
-
a
)
n
n
!
Doc 17
0.5470, -14.0000, 8.0000, 0.5470
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Wright_Omega_function.html
M
(
a
,
b
,
z
)
=
∑
n
=
0
∞
a
(
n
)
z
n
b
(
n
)
n
!
=
F
1
1
(
a
;
b
;
z
)
,
Doc 18
0.5470, -19.0000, 9.0000, 0.5470
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Confluent_hypergeometric_function.html
D
q
(
f
(
x
)
)
=
∑
k
=
0
∞
(
q
-
1
)
k
(
k
+
1
)
!
x
k
f
(
k
+
1
)
(
x
)
.
Doc 19
0.5291, -17.0000, 8.0000, 0.5291
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Q-derivative.html
P
=
∑
t
=
1
N
D
0
(
1
+
g
)
t
(
1
+
r
)
t
+
P
N
(
1
+
r
)
N
Doc 20
0.5240, -14.0000, 7.0000, 0.5240
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Dividend_discount_model.html
L
(
s
,
Δ
)
=
∑
n
=
1
∞
a
n
n
s
Doc 21
0.5076, -2.0000, 7.0000, 0.5076
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Selberg_class.html
L
(
E
,
s
)
=
∑
n
=
1
∞
a
n
n
s
.
Doc 22
0.5076, -3.0000, 7.0000, 0.5076
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Modularity_theorem.html
L
(
s
,
E
)
=
∑
n
=
1
∞
a
n
n
s
.
Doc 23
0.5076, -3.0000, 7.0000, 0.5076
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Modular_elliptic_curve.html
ψ
1
(
z
)
=
∑
n
=
0
∞
1
(
z
+
n
)
2
,
Doc 24
0.5076, -4.0000, 8.0000, 0.5076
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Trigamma_function.html
β
(
x
)
=
∑
k
=
0
∞
(
-
1
)
k
(
2
k
+
1
)
x
Doc 25
0.5076, -5.0000, 8.0000, 0.9391
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Clausen_function.html
β
(
s
)
=
∑
n
=
0
∞
(
-
1
)
n
(
2
n
+
1
)
s
,
Doc 26
0.5076, -6.0000, 8.0000, 0.5076
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Dirichlet_beta_function.html
f
(
x
)
=
∑
k
=
1
∞
sin
(
2
k
x
)
2
k
Doc 10
0.5470, -2.0000, 8.0000, 1.0462
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Draft:List_of_shape_topics_in_various_fields.html
Doc 27
0.4992, -3.0000, 7.0000, 0.4992
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/List_of_fractals_by_Hausdorff_dimension.html
L
(
M
,
V
,
s
)
=
∑
μ
∈
{
M
-
0
}
/
V
sign
N
(
μ
)
|
N
(
μ
)
|
s
Doc 28
0.4898, -7.0000, 7.0000, 0.4898
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Shimizu_L-function.html
f
(
i
1
,
…
,
i
n
)
=
∑
k
=
0
n
i
k
f
(
e
k
)
∈
I
p
Doc 29
0.4898, -9.0000, 7.0000, 0.4898
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Invariant_basis_number.html
G
(
a
,
0
,
c
)
=
∑
n
=
0
c
-
1
(
n
c
)
e
2
π
i
a
n
/
c
.
Doc 30
0.4898, -15.0000, 7.0000, 0.4898
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Quadratic_Gauss_sum.html
Mortgage Yield: ri such that P
=
∑
n
=
1
N
C
(
t
)
(
1
+
r
i
/
1200
)
t
-
1
Doc 31
0.4681, -3.0000, 7.0000, 0.4681
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Mortgage_yield.html
[
G
f
]
(
x
)
=
∑
n
=
1
∞
1
(
x
+
n
)
2
f
(
1
x
+
n
)
.
Doc 32
0.4681, -13.0000, 7.0000, 0.9186
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Gauss–Kuzmin–Wirsing_operator.html
H
N
,
q
,
s
=
∑
i
=
1
N
1
(
i
+
q
)
s
Doc 33
0.4505, -7.0000, 6.0000, 0.4505
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Zipf–Mandelbrot_law.html
t
n
=
∑
m
=
0
∞
G
m
n
(
m
+
1
)
(
m
+
2
)
.
Doc 32
0.4681, -13.0000, 7.0000, 0.9186
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Gauss–Kuzmin–Wirsing_operator.html
∑
n
=
1
∞
H
n
2
(
n
+
1
)
2
=
11
360
π
4
;
Doc 34
0.4505, -9.0000, 6.0000, 0.4505
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_number.html
∑
n
=
1
∞
H
¯
n
(
b
)
(
n
+
1
)
a
=
ζ
(
a
,
b
¯
)
Doc 6
0.6468, -4.0000, 8.0000, 1.0974
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Multiple_zeta_function.html
P
V
=
∑
t
=
1
n
F
V
t
(
1
+
i
)
t
Doc 35
0.4444, -4.0000, 6.0000, 0.4444
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Time_value_of_money.html
D
P
V
=
∑
t
=
0
N
F
V
t
(
1
+
r
)
t
Doc 36
0.4444, -5.0000, 7.0000, 0.4444
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Discounted_cash_flow.html
N
P
V
=
∑
n
=
0
N
C
n
(
1
+
r
)
n
=
0
Doc 37
0.4444, -6.0000, 7.0000, 0.4444
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Portal:Infrastructure::Economic_analysis.html
P
V
=
∑
k
=
1
∞
C
(
1
+
i
)
k
=
C
i
,
i
>
0
,
Doc 38
0.4444, -11.0000, 7.0000, 0.4444
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Present_value.html
H
V
[
i
,
n
]
=
∑
k
=
0
n
-
i
d
i
v
(
i
+
k
)
(
1
+
r
)
n
-
i
-
k
Doc 39
0.4444, -14.0000, 7.0000, 0.4444
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Holding_value.html
∫
0
∞
2
arctan
(
t
x
)
e
2
π
t
-
1
d
t
=
∑
n
=
1
∞
c
n
(
x
+
1
)
n
¯
Doc 40
0.4444, -19.0000, 7.0000, 0.4444
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Stirling's_approximation.html
Cl
2
m
(
q
π
p
)
=
∑
k
=
1
∞
sin
(
k
q
π
/
p
)
k
2
m
Doc 25
0.5076, -5.0000, 8.0000, 0.9391
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Clausen_function.html
f
(
x
)
=
∑
i
=
0
∞
x
2
i
Doc 41
0.4286, -1.0000, 6.0000, 0.4286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Closed-form_expression.html
P
0
=
∑
t
=
1
T
C
t
(
1
+
r
t
)
t
Doc 42
0.4286, -4.0000, 6.0000, 0.4286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Rational_pricing.html
NPV
=
∑
t
=
0
n
C
t
(
1
+
r
)
t
=
0
Doc 43
0.4286, -5.0000, 7.0000, 0.4286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Rate_of_return.html
NPV
=
∑
n
=
0
N
C
n
(
1
+
r
)
n
=
0
Doc 44
0.4286, -5.0000, 7.0000, 0.4286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Internal_rate_of_return.html
w
i
=
∑
j
=
2
n
a
j
(
i
+
1
)
j
,
Doc 45
0.4286, -5.0000, 6.0000, 0.4286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Distributed_lag.html
Z
=
∑
n
=
0
∞
(
(
2
n
)
!
)
3
(
42
n
+
5
)
(
n
!
)
6
16
3
n
+
1
Doc 46
0.4186, -14.0000, 8.0000, 1.2276
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
sinh
x
=
∑
n
=
0
∞
x
2
n
+
1
(
2
n
+
1
)
!
Doc 47
0.4045, -7.0000, 8.0000, 0.7286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hyperbolic_angle.html
Z
=
∑
n
=
0
∞
(
-
1
)
n
(
4
n
)
!
(
21460
n
+
1123
)
(
n
!
)
4
4
4
n
882
2
n
Doc 46
0.4186, -14.0000, 8.0000, 1.2276
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
Z
=
∑
n
=
0
∞
(
-
1
)
n
(
4
n
)
!
(
260
n
+
23
)
(
n
!
)
4
4
4
n
18
2
n
Doc 46
0.4186, -14.0000, 8.0000, 1.2276
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
1
n
=
∑
r
=
1
∞
1
(
n
+
1
)
r
.
Doc 48
0.3890, -6.0000, 7.0000, 0.3890
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Engel_expansion.html
cos
(
φ
)
=
∑
n
=
0
∞
(
-
φ
2
)
n
(
2
n
)
!
,
Doc 49
0.3890, -8.0000, 7.0000, 0.3890
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sine-Gordon_equation.html
∑
n
=
0
∞
1
(
n
+
a
)
Doc 50
0.3719, -1.0000, 7.0000, 0.3719
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Functional_determinant.html
φ
(
x
)
=
∑
i
∈
ℤ
s
i
(
x
-
i
)
k
Doc 51
0.3719, -4.0000, 4.0000, 0.3719
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Refinable_function.html
∑
n
=
0
∞
2
n
+
3
(
n
+
1
)
(
n
+
2
)
Doc 52
0.3719, -8.0000, 7.0000, 0.3719
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Telescoping_series.html
ϑ
00
(
z
,
q
)
=
∑
n
=
-
∞
∞
q
n
2
exp
(
2
π
i
n
z
)
Doc 53
0.3719, -13.0000, 5.0000, 0.6651
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Jacobi_theta_functions_(notational_variations).html
∑
n
=
0
∞
(
-
1
)
n
(
n
+
1
)
(
n
+
2
)
=
2
ln
2
-
1.
Doc 54
0.3719, -14.0000, 7.0000, 0.7212
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
L
=
P
∑
j
=
1
n
1
(
1
+
i
)
j
Doc 55
0.3644, -4.0000, 6.0000, 0.3644
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Compound_interest.html
∑
n
=
1
∞
$
100
(
1
+
I
)
n
,
Doc 56
0.3493, -4.0000, 6.0000, 0.3493
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Geometric_series.html
∑
k
=
0
∞
(
-
1
)
k
(
z
+
k
)
m
+
1
Doc 57
0.3493, -5.0000, 7.0000, 0.3493
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Polygamma_function.html
1
Q
=
∑
i
=
1
r
S
i
(
x
-
λ
i
)
ν
i
Doc 58
0.3493, -5.0000, 5.0000, 0.3493
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Chinese_remainder_theorem.html
P
Q
=
∑
j
=
1
r
A
j
(
x
-
λ
j
)
ν
j
Doc 59
0.3493, -5.0000, 5.0000, 0.3493
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Partial_fraction_decomposition.html
e
=
∑
k
=
0
∞
3
-
4
k
2
(
2
k
+
1
)
!
Doc 60
0.3493, -8.0000, 8.0000, 0.6190
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/List_of_representations_of_e.html
ζ
(
3
)
=
8
7
∑
k
=
0
∞
1
(
2
k
+
1
)
3
Doc 62
0.3493, -9.0000, 7.0000, 0.3493
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Apéry's_constant.html
∑
k
=
0
∞
z
2
k
+
1
(
2
k
+
1
)
!
=
sinh
z
Doc 61
0.3493, -9.0000, 7.0000, 0.6589
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/List_of_mathematical_series.html
∑
k
=
0
∞
1
(
2
k
+
1
)
2
=
π
2
2
3
=
π
2
8
Doc 63
0.3493, -13.0000, 7.0000, 0.6987
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Partial_fractions_in_complex_analysis.html
sinc
(
x
)
=
sin
(
x
)
x
=
∑
n
=
0
∞
(
-
x
2
)
n
(
2
n
+
1
)
!
Doc 64
0.3493, -16.0000, 8.0000, 0.3493
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Sinc_function.html
∑
k
=
0
∞
1
(
2
k
+
1
)
4
=
1
3
π
4
2
5
=
π
4
96
.
Doc 63
0.3493, -13.0000, 7.0000, 0.6987
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Partial_fractions_in_complex_analysis.html
∑
n
=
1
∞
(
-
1
)
n
+
1
n
=
∑
n
=
0
∞
1
(
2
n
+
1
)
(
2
n
+
2
)
=
ln
2.
Doc 54
0.3719, -14.0000, 7.0000, 0.7212
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
g
(
x
)
=
∑
n
=
1
∞
f
(
n
)
exp
(
2
π
i
n
x
)
Doc 65
0.3326, -10.0000, 4.0000, 0.3326
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Multiplication_theorem.html
f
(
α
)
=
∑
x
=
1
N
exp
(
2
π
i
P
(
x
)
α
)
,
Doc 66
0.3326, -10.0000, 3.0000, 0.3326
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Hua's_lemma.html
θ
^
F
(
z
)
=
∑
k
=
0
∞
R
F
(
k
)
exp
(
2
π
i
k
z
)
,
Doc 67
0.3326, -14.0000, 5.0000, 0.5863
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Theta_function.html
cosh
x
=
∑
n
=
0
∞
x
2
n
(
2
n
)
!
Doc 47
0.4045, -7.0000, 8.0000, 0.7286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hyperbolic_angle.html
λ
=
∫
0
∞
ρ
(
t
)
(
t
+
1
)
2
d
t
Doc 68
0.3241, -6.0000, 6.0000, 0.3241
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Golomb–Dickman_constant.html
τ
=
∑
i
=
0
∞
t
i
2
i
+
1
Doc 70
0.3096, -3.0000, 6.0000, 0.3096
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/List_of_OEIS_sequences.html
r
=
∑
i
=
0
∞
a
i
10
i
Doc 69
0.3096, -3.0000, 6.0000, 0.3096
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Decimal_representation.html
1
(
x
;
q
)
∞
=
∑
n
=
0
∞
x
n
(
q
;
q
)
n
Doc 71
0.3096, -10.0000, 7.0000, 0.5792
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Q-Pochhammer_symbol.html
∑
k
=
0
∞
(
-
1
)
k
z
2
k
+
1
(
2
k
+
1
)
!
=
sin
z
Doc 61
0.3493, -9.0000, 7.0000, 0.6589
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/List_of_mathematical_series.html
Φ
(
exp
(
2
π
i
λ
)
,
s
,
α
)
=
L
(
λ
,
α
,
s
)
.
Doc 1
1.0000, -1.0000, 17.0000, 2.5376
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lerch_zeta_function.html
λ
n
=
∑
m
(
1
+
n
2
)
k
-
1
2
(
1
+
m
2
+
n
2
)
k
.
Doc 72
0.2932, -14.0000, 5.0000, 0.2932
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Sobolev_spaces_for_planar_domains.html
P
m
(
Δ
,
x
)
=
exp
(
2
π
i
m
x
)
sin
(
π
m
Δ
)
π
m
.
Doc 73
0.2932, -15.0000, 6.0000, 0.2932
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Crenel_function.html
ϑ
0
,
0
(
x
)
=
∑
n
=
-
∞
∞
q
n
2
exp
(
2
π
i
n
x
/
a
)
Doc 53
0.3719, -13.0000, 5.0000, 0.6651
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Jacobi_theta_functions_(notational_variations).html
1
2
=
∑
k
=
0
∞
(
-
1
)
k
(
π
4
)
2
k
(
2
k
)
!
.
Doc 74
0.2835, -16.0000, 8.0000, 0.2835
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Square_root_of_2.html
e
=
∑
k
=
0
∞
(
3
k
)
2
+
1
(
3
k
)
!
Doc 60
0.3493, -8.0000, 8.0000, 0.6190
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/List_of_representations_of_e.html
π
2
sin
2
π
z
=
∑
n
=
-
∞
∞
1
(
z
-
n
)
2
.
Doc 75
0.2697, -12.0000, 6.0000, 0.2697
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sine.html
(
a
x
;
q
)
∞
(
x
;
q
)
∞
=
∑
n
=
0
∞
(
a
;
q
)
n
(
q
;
q
)
n
x
n
.
Doc 71
0.3096, -10.0000, 7.0000, 0.5792
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Q-Pochhammer_symbol.html
q
=
exp
(
2
π
i
/
N
)
Doc 76
0.2538, -2.0000, 5.0000, 0.2538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Volume_conjecture.html
z
=
exp
(
2
π
i
/
3
)
.
Doc 77
0.2538, -3.0000, 5.0000, 0.2538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Butson-type_Hadamard_matrix.html
S
=
∑
p
≤
P
exp
(
2
π
i
f
(
p
)
)
.
Doc 78
0.2538, -7.0000, 5.0000, 0.2538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Ivan_Matveyevich_Vinogradov.html
∑
n
=
1
k
χ
(
n
)
exp
(
2
π
i
n
/
k
)
.
Doc 13
0.5470, -3.0000, 8.0000, 0.8008
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_L-function.html
θ
F
(
z
)
=
∑
m
∈
Z
n
exp
(
2
π
i
z
F
(
m
)
)
Doc 67
0.3326, -14.0000, 5.0000, 0.5863
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Theta_function.html
1
sin
2
(
z
)
=
∑
n
∈
ℤ
1
(
z
-
n
π
)
2
Doc 79
0.2143, -10.0000, 4.0000, 0.2143
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Mittag-Leffler's_theorem.html
x
l
(
1
-
x
)
l
+
1
=
∑
p
=
0
∞
(
p
l
)
x
p
.
Doc 80
0.2143, -16.0000, 5.0000, 0.4286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html
1
(
1
-
z
)
α
+
1
=
∑
n
=
0
∞
(
n
+
α
n
)
z
n
Doc 80
0.2143, -16.0000, 5.0000, 0.4286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html
1
(
1
-
2
x
t
+
t
2
)
α
=
∑
n
=
0
∞
C
n
(
α
)
(
x
)
t
n
.
Doc 81
0.2143, -16.0000, 3.0000, 0.2143
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Gegenbauer_polynomials.html