tangent
Not Supported
L
(
λ
,
α
,
s
)
=
∑
n
=
0
∞
exp
(
2
π
i
λ
n
)
(
n
+
α
)
s
.
Search
Returned 96 matches (100 formulae, 81 docs)
Lookup 13.759 ms, Re-ranking 594.127 ms
Found 173014 tuple postings, 81772 formulae, 15774 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, 0.0000, 27.0000, 2.1436
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lerch_zeta_function.html
Φ
(
z
,
s
,
α
)
=
∑
n
=
0
∞
z
n
(
n
+
α
)
s
.
Doc 1
1.0000, 0.0000, 27.0000, 2.1436
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lerch_zeta_function.html
Doc 2
0.6400, -4.0000, 16.0000, 0.6400
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Catalan's_constant.html
Φ
(
z
,
s
,
q
)
=
∑
k
=
0
∞
z
k
(
k
+
q
)
s
Doc 3
0.6021, -4.0000, 12.0000, 1.8930
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Riemann_zeta_function.html
Doc 4
0.6021, -4.0000, 12.0000, 1.0825
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Hurwitz_zeta_function.html
Z
(
P
,
Q
,
s
)
=
∑
n
=
1
∞
f
n
(
P
)
f
n
(
Q
)
λ
n
s
Doc 5
0.6021, -8.0000, 12.0000, 0.9383
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Minakshisundaram–Pleijel_zeta_function.html
Z
(
λ
,
ν
)
=
∑
j
=
0
∞
λ
j
(
j
!
)
ν
.
Doc 6
0.5469, -4.0000, 10.0000, 0.5469
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Conway–Maxwell–Poisson_distribution.html
ζ
(
s
,
a
)
=
∑
n
=
0
∞
1
(
n
+
a
)
s
Doc 7
0.5424, -2.0000, 12.0000, 0.5424
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Ramanujan's_master_theorem.html
ζ
(
s
,
q
)
=
∑
k
=
0
∞
1
(
k
+
q
)
s
Doc 3
0.6021, -4.0000, 12.0000, 1.8930
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Riemann_zeta_function.html
ζ
(
s
,
t
)
=
∑
n
=
1
∞
H
n
,
t
(
n
+
1
)
s
Doc 8
0.5424, -5.0000, 11.0000, 0.5424
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 9
0.5263, -11.0000, 9.0000, 0.8084
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_polynomials.html
L
(
E
,
s
)
=
∑
n
=
1
∞
a
n
n
s
.
Doc 10
0.4884, -3.0000, 10.0000, 0.4884
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Modularity_theorem.html
ζ
(
s
,
q
)
=
∑
n
=
0
∞
1
(
q
+
n
)
s
.
Doc 4
0.6021, -4.0000, 12.0000, 1.0825
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Hurwitz_zeta_function.html
f
(
x
)
=
∑
n
=
0
∞
s
(
2
n
x
)
2
n
Doc 11
0.4713, -4.0000, 9.0000, 0.4713
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Draft:List_of_shape_topics_in_various_fields.html
blanc
(
x
)
=
∑
n
=
0
∞
s
(
2
n
x
)
2
n
,
Doc 12
0.4713, -5.0000, 9.0000, 0.4713
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Blancmange_curve.html
Ξ
(
μ
,
V
,
β
)
=
∑
n
=
0
∞
e
β
μ
n
Z
(
n
,
V
,
β
)
,
Doc 13
0.4713, -12.0000, 9.0000, 0.4713
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Polymer_field_theory.html
L
(
M
,
V
,
s
)
=
∑
μ
∈
{
M
-
0
}
/
V
sign
N
(
μ
)
|
N
(
μ
)
|
s
Doc 14
0.4713, -14.0000, 9.0000, 0.4713
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Shimizu_L-function.html
NPV
(
i
,
N
)
=
∑
t
=
0
N
R
t
(
1
+
i
)
t
Doc 15
0.4660, -5.0000, 8.0000, 0.8936
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Net_present_value.html
Mortgage Yield: ri such that P
=
∑
n
=
1
N
C
(
t
)
(
1
+
r
i
/
1200
)
t
-
1
Doc 16
0.4504, -8.0000, 8.0000, 0.4504
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Mortgage_yield.html
L
(
s
,
E
)
=
∑
n
=
1
∞
a
n
n
s
.
Doc 17
0.4416, -3.0000, 10.0000, 0.4416
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Modular_elliptic_curve.html
S
ρ
(
z
)
=
∑
n
=
0
∞
m
n
z
n
+
1
.
Doc 18
0.4335, -6.0000, 8.0000, 0.4335
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Stieltjes_transformation.html
F
(
w
)
=
∑
n
=
0
∞
f
n
Ψ
n
w
n
+
1
.
Doc 19
0.4335, -7.0000, 8.0000, 0.8292
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Nachbin's_theorem.html
H
N
,
q
,
s
=
∑
i
=
1
N
1
(
i
+
q
)
s
Doc 20
0.4335, -7.0000, 7.0000, 0.4335
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 21
0.4335, -9.0000, 9.0000, 0.4335
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Gauss–Kuzmin–Wirsing_operator.html
L
(
χ
,
s
)
=
∑
n
=
1
∞
χ
(
n
)
n
s
Doc 22
0.4276, -4.0000, 10.0000, 0.4276
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Generalized_Riemann_hypothesis.html
NPV
(
i
)
=
∑
t
=
0
N
R
t
(
1
+
i
)
t
Doc 15
0.4660, -5.0000, 8.0000, 0.8936
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Net_present_value.html
L
(
s
,
χ
)
=
∑
n
=
1
∞
χ
(
n
)
n
s
.
Doc 23
0.4152, -4.0000, 11.0000, 0.4152
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_L-function.html
φ
(
s
)
=
∑
n
=
1
∞
a
n
n
s
.
Doc 26
0.4124, -3.0000, 8.0000, 0.4124
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Ramanujan–Petersson_conjecture.html
F
(
s
)
=
∑
n
=
1
∞
f
(
n
)
n
s
Doc 24
0.4124, -3.0000, 8.0000, 3.6283
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
Doc 27
0.4124, -3.0000, 8.0000, 0.4124
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Von_Mangoldt_function.html
g
(
s
)
=
∑
n
=
1
∞
a
(
n
)
n
s
Doc 25
0.4124, -3.0000, 8.0000, 0.4124
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Perron's_formula.html
ζ
2
(
s
)
=
∑
n
=
1
∞
d
(
n
)
n
s
Doc 24
0.4124, -3.0000, 8.0000, 3.6283
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
log
2
=
∑
n
=
1
∞
ζ
(
2
n
)
-
1
n
.
Doc 3
0.6021, -4.0000, 12.0000, 1.8930
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Riemann_zeta_function.html
ψ
1
(
z
)
=
∑
n
=
0
∞
1
(
z
+
n
)
2
,
Doc 28
0.4124, -6.0000, 9.0000, 0.4124
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Trigamma_function.html
F
χ
(
s
)
=
∑
n
=
1
∞
χ
(
n
)
a
n
n
s
Doc 29
0.4124, -6.0000, 8.0000, 0.8151
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Selberg_class.html
L
(
s
,
Δ
)
=
∑
n
=
1
∞
a
n
n
s
Doc 29
0.4124, -6.0000, 8.0000, 0.8151
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Selberg_class.html
exp
(
z
)
=
∑
n
=
0
∞
z
n
n
!
.
Doc 30
0.3957, -4.0000, 8.0000, 0.7914
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/P-adic_exponential_function.html
exp
p
(
z
)
=
∑
n
=
0
∞
z
n
n
!
.
Doc 30
0.3957, -4.0000, 8.0000, 0.7914
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/P-adic_exponential_function.html
e
q
x
=
∑
n
=
0
∞
x
n
[
n
]
q
!
.
Doc 31
0.3957, -6.0000, 9.0000, 0.3957
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Q-analog.html
R
=
exp
(
A
)
=
∑
n
=
0
∞
A
n
n
!
.
Doc 32
0.3957, -6.0000, 8.0000, 0.3957
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Skew-symmetric_matrix.html
f
(
x
)
=
∑
n
=
0
∞
a
n
M
(
n
+
1
)
x
n
Doc 19
0.4335, -7.0000, 8.0000, 0.8292
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Nachbin's_theorem.html
f
(
t
)
=
∑
n
=
0
∞
a
n
M
(
n
+
1
)
x
n
Doc 33
0.3957, -8.0000, 7.0000, 0.3957
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Integral_equation.html
cos
(
φ
)
=
∑
n
=
0
∞
(
-
φ
2
)
n
(
2
n
)
!
,
Doc 34
0.3957, -9.0000, 8.0000, 0.3957
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sine-Gordon_equation.html
β
(
s
)
=
∑
n
=
0
∞
(
-
1
)
n
(
2
n
+
1
)
s
,
Doc 35
0.3957, -10.0000, 9.0000, 0.3957
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Dirichlet_beta_function.html
D
G
(
f
;
s
)
=
∑
n
=
1
∞
f
(
n
)
n
s
Doc 36
0.3892, -6.0000, 8.0000, 0.3892
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Dirichlet_convolution.html
N
P
V
=
∑
n
=
0
N
C
n
(
1
+
r
)
n
=
0
Doc 37
0.3892, -7.0000, 8.0000, 0.3892
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Portal:Infrastructure::Economic_analysis.html
x
x
=
exp
(
x
log
x
)
=
∑
n
=
0
∞
x
n
(
log
x
)
n
n
!
.
Doc 38
0.3892, -12.0000, 9.0000, 0.3892
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sophomore's_dream.html
L
(
s
,
χ
)
=
∑
n
=
1
∞
χ
(
n
)
n
s
Doc 39
0.3755, -4.0000, 10.0000, 0.3755
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Dirichlet_character.html
L
(
s
,
a
)
=
∑
n
=
1
∞
a
(
n
)
n
s
=
∏
p
(
1
-
a
(
p
)
p
s
)
-
1
,
Doc 40
0.3755, -19.0000, 10.0000, 0.3755
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Completely_multiplicative_function.html
ζ
(
s
)
=
∑
n
=
1
∞
1
n
s
.
Doc 41
0.3743, -3.0000, 8.0000, 0.5951
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
Doc 42
0.3743, -3.0000, 8.0000, 0.3743
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/List_of_zeta_functions.html
Doc 43
0.3743, -3.0000, 8.0000, 0.3743
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Basel_problem.html
ζ
S
(
s
)
=
∑
n
=
1
∞
1
λ
n
s
.
Doc 44
0.3743, -5.0000, 8.0000, 0.7321
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Functional_determinant.html
1
n
=
∑
r
=
1
∞
1
(
n
+
1
)
r
.
Doc 45
0.3743, -6.0000, 9.0000, 0.3743
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Engel_expansion.html
NPV
=
∑
n
=
0
N
C
n
(
1
+
r
)
n
=
0
Doc 46
0.3743, -6.0000, 8.0000, 0.3743
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Internal_rate_of_return.html
DG
(
a
n
;
s
)
=
∑
n
=
1
∞
a
n
n
s
.
Doc 47
0.3743, -7.0000, 8.0000, 0.6943
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Generating_function.html
ζ
(
2
s
)
ζ
(
s
)
=
∑
n
=
1
∞
λ
(
n
)
n
s
.
Doc 24
0.4124, -3.0000, 8.0000, 3.6283
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
Doc 48
0.3743, -10.0000, 9.0000, 0.3743
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Liouville_function.html
ζ
4
(
s
)
ζ
(
2
s
)
=
∑
n
=
1
∞
d
(
n
)
2
n
s
.
Doc 24
0.4124, -3.0000, 8.0000, 3.6283
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
σ
1
-
s
(
m
)
ζ
(
s
)
=
∑
n
=
1
∞
c
n
(
m
)
n
s
.
Doc 24
0.4124, -3.0000, 8.0000, 3.6283
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
Z
=
∑
n
=
0
∞
(
(
2
n
)
!
)
3
(
42
n
+
5
)
(
n
!
)
6
16
3
n
+
1
Doc 49
0.3743, -17.0000, 10.0000, 1.7185
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
G
(
a
,
0
,
c
)
=
∑
n
=
0
c
-
1
(
n
c
)
e
2
π
i
a
n
/
c
.
Doc 50
0.3743, -17.0000, 8.0000, 0.3743
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Quadratic_Gauss_sum.html
Z
=
∑
n
=
0
∞
(
-
1
)
n
(
4
n
)
!
(
21460
n
+
1123
)
(
n
!
)
4
4
4
n
882
2
n
Doc 49
0.3743, -17.0000, 10.0000, 1.7185
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 49
0.3743, -17.0000, 10.0000, 1.7185
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
∑
n
=
0
∞
1
(
n
+
a
)
Doc 44
0.3743, -5.0000, 8.0000, 0.7321
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Functional_determinant.html
exp
(
ν
)
=
∑
n
=
0
∞
ν
*
n
n
!
Doc 51
0.3579, -5.0000, 7.0000, 0.3579
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Compound_Poisson_process.html
e
1
-
e
x
=
∑
n
=
0
∞
A
n
(
x
)
n
!
(
1
-
x
)
n
+
1
.
Doc 52
0.3579, -17.0000, 9.0000, 0.3579
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Eulerian_number.html
NPV
=
∑
t
=
0
n
C
t
(
1
+
r
)
t
=
0
Doc 53
0.3506, -6.0000, 7.0000, 0.3506
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Rate_of_return.html
cosh
x
=
∑
n
=
0
∞
x
2
n
(
2
n
)
!
Doc 54
0.3361, -6.0000, 8.0000, 0.6723
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hyperbolic_angle.html
1
ζ
(
s
)
=
∑
n
=
1
∞
μ
(
n
)
n
s
Doc 3
0.6021, -4.0000, 12.0000, 1.8930
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Riemann_zeta_function.html
Doc 24
0.4124, -3.0000, 8.0000, 3.6283
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
Doc 55
0.3361, -7.0000, 8.0000, 0.3361
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Riemann_hypothesis.html
1
ζ
(
s
)
=
∑
n
=
1
∞
μ
(
n
)
n
s
,
Doc 56
0.3361, -8.0000, 8.0000, 0.3361
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Mertens_conjecture.html
sinh
x
=
∑
n
=
0
∞
x
2
n
+
1
(
2
n
+
1
)
!
Doc 54
0.3361, -6.0000, 8.0000, 0.6723
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hyperbolic_angle.html
Z
(
s
)
=
∑
n
≠
0
1
(
n
2
)
s
=
2
ζ
(
2
s
)
Doc 5
0.6021, -8.0000, 12.0000, 0.9383
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Minakshisundaram–Pleijel_zeta_function.html
ζ
(
s
-
1
)
ζ
(
s
)
=
∑
n
=
1
∞
φ
(
n
)
n
s
Doc 24
0.4124, -3.0000, 8.0000, 3.6283
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
1
(
x
;
q
)
∞
=
∑
n
=
0
∞
x
n
(
q
;
q
)
n
Doc 57
0.3361, -11.0000, 8.0000, 0.3361
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Q-Pochhammer_symbol.html
ζ
3
(
s
)
ζ
(
2
s
)
=
∑
n
=
1
∞
d
(
n
2
)
n
s
Doc 24
0.4124, -3.0000, 8.0000, 3.6283
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
ζ
(
s
-
k
)
ζ
(
s
)
=
∑
n
=
1
∞
J
k
(
n
)
n
s
Doc 24
0.4124, -3.0000, 8.0000, 3.6283
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
1
L
(
χ
,
s
)
=
∑
n
=
1
∞
μ
(
n
)
χ
(
n
)
n
s
Doc 24
0.4124, -3.0000, 8.0000, 3.6283
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
1
2
=
∑
k
=
0
∞
(
-
1
)
k
(
π
4
)
2
k
(
2
k
)
!
.
Doc 58
0.3361, -16.0000, 9.0000, 0.3361
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Square_root_of_2.html
Z
=
∑
n
=
0
∞
(
8
n
+
1
)
(
1
2
)
n
(
1
4
)
n
(
3
4
)
n
(
n
!
)
3
9
n
Doc 49
0.3743, -17.0000, 10.0000, 1.7185
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
x
=
∑
n
=
0
∞
a
n
10
n
.
Doc 59
0.3200, -4.0000, 8.0000, 0.3200
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Hermite's_problem.html
e
x
=
∑
n
=
0
∞
x
n
n
!
.
Doc 60
0.3200, -5.0000, 8.0000, 0.3200
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Factorial.html
Doc 61
0.3200, -5.0000, 8.0000, 0.3200
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Auxiliary_function.html
E
=
∑
n
=
1
∞
σ
0
(
n
)
2
n
Doc 62
0.3200, -5.0000, 7.0000, 0.3200
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Erdős–Borwein_constant.html
exp
X
=
e
X
=
∑
n
=
0
∞
X
n
n
!
.
Doc 63
0.3200, -8.0000, 8.0000, 0.3200
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Baker–Campbell–Hausdorff_formula.html
∑
n
=
0
∞
2
n
+
3
(
n
+
1
)
(
n
+
2
)
Doc 64
0.3200, -9.0000, 9.0000, 0.3200
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Telescoping_series.html
g
(
x
)
=
∑
n
=
1
∞
f
(
n
)
exp
(
2
π
i
n
x
)
Doc 65
0.3200, -10.0000, 5.0000, 0.3200
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Multiplication_theorem.html
e
x
f
(
t
)
=
∑
n
=
0
∞
p
n
(
x
)
n
!
t
n
Doc 47
0.3743, -7.0000, 8.0000, 0.6943
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Generating_function.html
∑
n
=
0
∞
u
n
=
∑
n
=
0
∞
p
(
n
)
q
(
n
)
,
Doc 66
0.3200, -12.0000, 8.0000, 0.3200
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Digamma_function.html
∑
n
=
0
∞
(
-
1
)
n
(
n
+
1
)
(
n
+
2
)
=
2
ln
2
-
1.
Doc 67
0.3200, -15.0000, 9.0000, 0.3200
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
e
x
=
∑
n
=
0
∞
x
n
n
!
Doc 68
0.2821, -5.0000, 7.0000, 0.2821
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Exponentiation.html
Doc 69
0.2821, -5.0000, 7.0000, 0.2821
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Frequency_mixer.html
Doc 70
0.2821, -5.0000, 7.0000, 0.2821
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Real_number.html
e
z
=
∑
n
=
0
∞
z
n
n
!
Doc 71
0.2821, -5.0000, 7.0000, 0.2821
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Exponential_function.html
π
2
sin
2
π
z
=
∑
n
=
-
∞
∞
1
(
z
-
n
)
2
.
Doc 72
0.2821, -14.0000, 8.0000, 0.2821
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sine.html
D
e
D
-
1
=
log
(
Δ
+
1
)
Δ
=
∑
n
=
0
∞
(
-
Δ
)
n
n
+
1
.
Doc 9
0.5263, -11.0000, 9.0000, 0.8084
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_polynomials.html
L
χ
(
s
)
=
∑
χ
(
n
)
a
n
n
s
Doc 73
0.2595, -6.0000, 6.0000, 0.2595
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Converse_theorem.html
(
1
-
X
)
-
1
=
∑
n
=
0
∞
X
n
.
Doc 74
0.2595, -7.0000, 7.0000, 0.2595
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Formal_power_series.html
ζ
(
s
)
ζ
(
2
s
)
=
∑
n
=
1
∞
|
μ
(
n
)
|
n
s
Doc 75
0.2595, -13.0000, 7.0000, 0.2595
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Square-free_integer.html
Φ
(
exp
(
2
π
i
λ
)
,
s
,
α
)
=
L
(
λ
,
α
,
s
)
.
Doc 1
1.0000, 0.0000, 27.0000, 2.1436
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lerch_zeta_function.html
Z
=
∑
n
=
0
∞
(
6
n
+
1
)
(
1
2
)
n
3
4
n
(
n
!
)
3
Doc 49
0.3743, -17.0000, 10.0000, 1.7185
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
L
(
λ
,
α
,
s
)
Doc 1
1.0000, 0.0000, 27.0000, 2.1436
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lerch_zeta_function.html
e
=
∑
n
=
0
∞
1
n
!
Doc 76
0.2442, -4.0000, 7.0000, 0.2442
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/E_(mathematical_constant).html
e
=
∑
n
=
0
∞
1
n
!
⋅
Doc 77
0.2442, -5.0000, 7.0000, 0.2442
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Proof_that_e_is_irrational.html
e
=
∑
n
=
0
∞
1
n
!
≈
2.71828
Doc 78
0.2442, -6.0000, 7.0000, 0.2442
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Dimensionless_quantity.html
1
1
-
w
=
∑
n
=
0
∞
w
n
.
Doc 79
0.2208, -7.0000, 7.0000, 0.2208
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Asymptotic_expansion.html
𝐀
-
1
=
∑
n
=
0
∞
(
𝐈
-
𝐀
)
n
.
Doc 80
0.2208, -8.0000, 7.0000, 0.2208
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Invertible_matrix.html
∑
n
=
0
∞
a
σ
(
n
)
=
∑
n
=
0
∞
a
n
.
Doc 41
0.3743, -3.0000, 8.0000, 0.5951
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
1
(
1
-
z
)
α
+
1
=
∑
n
=
0
∞
(
n
+
α
n
)
z
n
Doc 81
0.2062, -16.0000, 6.0000, 0.2062
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html