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 1394.629 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, 1.9451
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, 1.9451
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lerch_zeta_function.html
Doc 2
0.5579, 0.5579
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Catalan's_constant.html
ζ
(
s
,
a
)
=
∑
n
=
0
∞
1
(
n
+
a
)
s
Doc 3
0.4533, 0.4533
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Ramanujan's_master_theorem.html
Φ
(
z
,
s
,
q
)
=
∑
k
=
0
∞
z
k
(
k
+
q
)
s
Doc 4
0.4518, 1.3635
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Riemann_zeta_function.html
Doc 5
0.4518, 0.8399
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Hurwitz_zeta_function.html
ζ
(
s
,
q
)
=
∑
k
=
0
∞
1
(
k
+
q
)
s
Doc 4
0.4518, 1.3635
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Riemann_zeta_function.html
ζ
(
s
,
q
)
=
∑
n
=
0
∞
1
(
q
+
n
)
s
.
Doc 5
0.4518, 0.8399
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Hurwitz_zeta_function.html
ζ
(
s
,
t
)
=
∑
n
=
1
∞
H
n
,
t
(
n
+
1
)
s
Doc 6
0.3830, 0.3830
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Multiple_zeta_function.html
L
(
s
,
χ
)
=
∑
n
=
1
∞
χ
(
n
)
n
s
.
Doc 7
0.3744, 0.3744
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_L-function.html
L
(
E
,
s
)
=
∑
n
=
1
∞
a
n
n
s
.
Doc 8
0.3725, 0.3725
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Modularity_theorem.html
L
(
s
,
E
)
=
∑
n
=
1
∞
a
n
n
s
.
Doc 9
0.3676, 0.3676
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Modular_elliptic_curve.html
f
(
x
)
=
∑
n
=
0
∞
s
(
2
n
x
)
2
n
Doc 10
0.3611, 0.3611
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 11
0.3529, 0.3529
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Blancmange_curve.html
Z
(
P
,
Q
,
s
)
=
∑
n
=
1
∞
f
n
(
P
)
f
n
(
Q
)
λ
n
s
Doc 12
0.3488, 0.5854
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Minakshisundaram–Pleijel_zeta_function.html
L
(
χ
,
s
)
=
∑
n
=
1
∞
χ
(
n
)
n
s
Doc 13
0.3447, 0.3447
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Generalized_Riemann_hypothesis.html
L
(
s
,
χ
)
=
∑
n
=
1
∞
χ
(
n
)
n
s
Doc 14
0.3398, 0.3398
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Dirichlet_character.html
Z
(
λ
,
ν
)
=
∑
j
=
0
∞
λ
j
(
j
!
)
ν
.
Doc 15
0.3318, 0.3318
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Conway–Maxwell–Poisson_distribution.html
L
(
s
,
Δ
)
=
∑
n
=
1
∞
a
n
n
s
Doc 16
0.3317, 0.6233
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Selberg_class.html
F
(
s
)
=
∑
n
=
1
∞
f
(
n
)
n
s
Doc 17
0.3150, 2.3229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
Doc 18
0.3150, 0.3150
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Von_Mangoldt_function.html
g
(
s
)
=
∑
n
=
1
∞
a
(
n
)
n
s
Doc 19
0.3150, 0.3150
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Perron's_formula.html
ζ
2
(
s
)
=
∑
n
=
1
∞
d
(
n
)
n
s
Doc 17
0.3150, 2.3229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
φ
(
s
)
=
∑
n
=
1
∞
a
n
n
s
.
Doc 20
0.3131, 0.3131
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Ramanujan–Petersson_conjecture.html
NPV
(
i
,
N
)
=
∑
t
=
0
N
R
t
(
1
+
i
)
t
Doc 21
0.3045, 0.6036
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Net_present_value.html
ψ
1
(
z
)
=
∑
n
=
0
∞
1
(
z
+
n
)
2
,
Doc 22
0.3037, 0.3037
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Trigamma_function.html
NPV
(
i
)
=
∑
t
=
0
N
R
t
(
1
+
i
)
t
Doc 21
0.3045, 0.6036
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Net_present_value.html
ζ
(
s
)
=
∑
n
=
1
∞
1
n
s
.
Doc 23
0.2969, 0.4507
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
Doc 24
0.2969, 0.2969
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/List_of_zeta_functions.html
Doc 25
0.2969, 0.2969
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Basel_problem.html
F
χ
(
s
)
=
∑
n
=
1
∞
χ
(
n
)
a
n
n
s
Doc 16
0.3317, 0.6233
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Selberg_class.html
S
ν
(
x
)
=
∑
k
=
0
∞
sin
(
(
2
k
+
1
)
π
x
)
(
2
k
+
1
)
ν
Doc 26
0.2867, 0.4200
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_polynomials.html
ζ
S
(
s
)
=
∑
n
=
1
∞
1
λ
n
s
.
Doc 27
0.2864, 0.5364
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Functional_determinant.html
log
2
=
∑
n
=
1
∞
ζ
(
2
n
)
-
1
n
.
Doc 4
0.4518, 1.3635
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Riemann_zeta_function.html
S
ρ
(
z
)
=
∑
n
=
0
∞
m
n
z
n
+
1
.
Doc 28
0.2804, 0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Stieltjes_transformation.html
exp
(
z
)
=
∑
n
=
0
∞
z
n
n
!
.
Doc 29
0.2778, 0.5542
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/P-adic_exponential_function.html
exp
p
(
z
)
=
∑
n
=
0
∞
z
n
n
!
.
Doc 29
0.2778, 0.5542
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/P-adic_exponential_function.html
1
n
=
∑
r
=
1
∞
1
(
n
+
1
)
r
.
Doc 30
0.2677, 0.2677
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Engel_expansion.html
D
G
(
f
;
s
)
=
∑
n
=
1
∞
f
(
n
)
n
s
Doc 31
0.2634, 0.2634
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Dirichlet_convolution.html
F
(
w
)
=
∑
n
=
0
∞
f
n
Ψ
n
w
n
+
1
.
Doc 32
0.2632, 0.4912
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Nachbin's_theorem.html
β
(
s
)
=
∑
n
=
0
∞
(
-
1
)
n
(
2
n
+
1
)
s
,
Doc 33
0.2614, 0.2614
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Dirichlet_beta_function.html
H
N
,
q
,
s
=
∑
i
=
1
N
1
(
i
+
q
)
s
Doc 34
0.2609, 0.2609
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Zipf–Mandelbrot_law.html
N
P
V
=
∑
n
=
0
N
C
n
(
1
+
r
)
n
=
0
Doc 35
0.2531, 0.2531
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Portal:Infrastructure::Economic_analysis.html
e
q
x
=
∑
n
=
0
∞
x
n
[
n
]
q
!
.
Doc 36
0.2513, 0.2513
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Q-analog.html
∑
n
=
0
∞
1
(
n
+
a
)
Doc 27
0.2864, 0.5364
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Functional_determinant.html
NPV
=
∑
n
=
0
N
C
n
(
1
+
r
)
n
=
0
Doc 37
0.2427, 0.2427
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Internal_rate_of_return.html
x
x
=
exp
(
x
log
x
)
=
∑
n
=
0
∞
x
n
(
log
x
)
n
n
!
.
Doc 38
0.2419, 0.2419
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sophomore's_dream.html
Ξ
(
μ
,
V
,
β
)
=
∑
n
=
0
∞
e
β
μ
n
Z
(
n
,
V
,
β
)
,
Doc 39
0.2405, 0.2405
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Polymer_field_theory.html
R
=
exp
(
A
)
=
∑
n
=
0
∞
A
n
n
!
.
Doc 40
0.2402, 0.2402
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Skew-symmetric_matrix.html
cos
(
φ
)
=
∑
n
=
0
∞
(
-
φ
2
)
n
(
2
n
)
!
,
Doc 41
0.2371, 0.2371
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sine-Gordon_equation.html
Z
(
s
)
=
∑
n
≠
0
1
(
n
2
)
s
=
2
ζ
(
2
s
)
Doc 12
0.3488, 0.5854
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Minakshisundaram–Pleijel_zeta_function.html
t
n
=
∑
m
=
0
∞
G
m
n
(
m
+
1
)
(
m
+
2
)
.
Doc 42
0.2358, 0.2358
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Gauss–Kuzmin–Wirsing_operator.html
exp
(
ν
)
=
∑
n
=
0
∞
ν
*
n
n
!
Doc 43
0.2350, 0.2350
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Compound_Poisson_process.html
Mortgage Yield: ri such that P
=
∑
n
=
1
N
C
(
t
)
(
1
+
r
i
/
1200
)
t
-
1
Doc 44
0.2346, 0.2346
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Mortgage_yield.html
ζ
(
2
s
)
ζ
(
s
)
=
∑
n
=
1
∞
λ
(
n
)
n
s
.
Doc 17
0.3150, 2.3229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
Doc 45
0.2341, 0.2341
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Liouville_function.html
DG
(
a
n
;
s
)
=
∑
n
=
1
∞
a
n
n
s
.
Doc 46
0.2308, 0.4222
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Generating_function.html
L
(
M
,
V
,
s
)
=
∑
μ
∈
{
M
-
0
}
/
V
sign
N
(
μ
)
|
N
(
μ
)
|
s
Doc 47
0.2302, 0.2302
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Shimizu_L-function.html
L
(
λ
,
α
,
s
)
Doc 1
1.0000, 1.9451
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lerch_zeta_function.html
f
(
x
)
=
∑
n
=
0
∞
a
n
M
(
n
+
1
)
x
n
Doc 32
0.2632, 0.4912
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 48
0.2281, 0.2281
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Integral_equation.html
cosh
x
=
∑
n
=
0
∞
x
2
n
(
2
n
)
!
Doc 49
0.2275, 0.4234
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hyperbolic_angle.html
ζ
4
(
s
)
ζ
(
2
s
)
=
∑
n
=
1
∞
d
(
n
)
2
n
s
.
Doc 17
0.3150, 2.3229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
NPV
=
∑
t
=
0
n
C
t
(
1
+
r
)
t
=
0
Doc 50
0.2233, 0.2233
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Rate_of_return.html
σ
1
-
s
(
m
)
ζ
(
s
)
=
∑
n
=
1
∞
c
n
(
m
)
n
s
.
Doc 17
0.3150, 2.3229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
1
ζ
(
s
)
=
∑
n
=
1
∞
μ
(
n
)
n
s
Doc 4
0.4518, 1.3635
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Riemann_zeta_function.html
Doc 17
0.3150, 2.3229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
Doc 51
0.2187, 0.2187
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Riemann_hypothesis.html
1
ζ
(
s
)
=
∑
n
=
1
∞
μ
(
n
)
n
s
,
Doc 52
0.2143, 0.2143
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Mertens_conjecture.html
L
χ
(
s
)
=
∑
χ
(
n
)
a
n
n
s
Doc 53
0.2132, 0.2132
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Converse_theorem.html
x
=
∑
n
=
0
∞
a
n
10
n
.
Doc 54
0.2131, 0.2131
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Hermite's_problem.html
e
x
=
∑
n
=
0
∞
x
n
n
!
.
Doc 55
0.2120, 0.2120
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Factorial.html
Doc 56
0.2120, 0.2120
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Auxiliary_function.html
(
1
-
X
)
-
1
=
∑
n
=
0
∞
X
n
.
Doc 57
0.2079, 0.2079
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Formal_power_series.html
1
(
x
;
q
)
∞
=
∑
n
=
0
∞
x
n
(
q
;
q
)
n
Doc 58
0.2048, 0.2048
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Q-Pochhammer_symbol.html
L
(
s
,
a
)
=
∑
n
=
1
∞
a
(
n
)
n
s
=
∏
p
(
1
-
a
(
p
)
p
s
)
-
1
,
Doc 59
0.2047, 0.2047
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Completely_multiplicative_function.html
ζ
(
s
-
1
)
ζ
(
s
)
=
∑
n
=
1
∞
φ
(
n
)
n
s
Doc 17
0.3150, 2.3229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
ζ
3
(
s
)
ζ
(
2
s
)
=
∑
n
=
1
∞
d
(
n
2
)
n
s
Doc 17
0.3150, 2.3229
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 17
0.3150, 2.3229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
sinh
x
=
∑
n
=
0
∞
x
2
n
+
1
(
2
n
+
1
)
!
Doc 49
0.2275, 0.4234
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hyperbolic_angle.html
e
x
f
(
t
)
=
∑
n
=
0
∞
p
n
(
x
)
n
!
t
n
Doc 46
0.2308, 0.4222
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Generating_function.html
Z
=
∑
n
=
0
∞
(
(
2
n
)
!
)
3
(
42
n
+
5
)
(
n
!
)
6
16
3
n
+
1
Doc 60
0.1901, 0.8291
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
1
L
(
χ
,
s
)
=
∑
n
=
1
∞
μ
(
n
)
χ
(
n
)
n
s
Doc 17
0.3150, 2.3229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
E
=
∑
n
=
1
∞
σ
0
(
n
)
2
n
Doc 61
0.1895, 0.1895
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Erdős–Borwein_constant.html
∑
n
=
0
∞
2
n
+
3
(
n
+
1
)
(
n
+
2
)
Doc 62
0.1856, 0.1856
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Telescoping_series.html
e
x
=
∑
n
=
0
∞
x
n
n
!
Doc 63
0.1833, 0.1833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Exponentiation.html
Doc 64
0.1833, 0.1833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Frequency_mixer.html
Doc 65
0.1833, 0.1833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Real_number.html
e
z
=
∑
n
=
0
∞
z
n
n
!
Doc 66
0.1833, 0.1833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Exponential_function.html
∑
n
=
0
∞
u
n
=
∑
n
=
0
∞
p
(
n
)
q
(
n
)
,
Doc 67
0.1826, 0.1826
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Digamma_function.html
G
(
a
,
0
,
c
)
=
∑
n
=
0
c
-
1
(
n
c
)
e
2
π
i
a
n
/
c
.
Doc 68
0.1812, 0.1812
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Quadratic_Gauss_sum.html
1
2
=
∑
k
=
0
∞
(
-
1
)
k
(
π
4
)
2
k
(
2
k
)
!
.
Doc 69
0.1781, 0.1781
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Square_root_of_2.html
e
1
-
e
x
=
∑
n
=
0
∞
A
n
(
x
)
n
!
(
1
-
x
)
n
+
1
.
Doc 70
0.1776, 0.1776
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Eulerian_number.html
Z
=
∑
n
=
0
∞
(
-
1
)
n
(
4
n
)
!
(
21460
n
+
1123
)
(
n
!
)
4
4
4
n
882
2
n
Doc 60
0.1901, 0.8291
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 60
0.1901, 0.8291
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
e
=
∑
n
=
0
∞
1
n
!
Doc 71
0.1724, 0.1724
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/E_(mathematical_constant).html
1
1
-
w
=
∑
n
=
0
∞
w
n
.
Doc 72
0.1705, 0.1705
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Asymptotic_expansion.html
exp
X
=
e
X
=
∑
n
=
0
∞
X
n
n
!
.
Doc 73
0.1703, 0.1703
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Baker–Campbell–Hausdorff_formula.html
e
=
∑
n
=
0
∞
1
n
!
⋅
Doc 74
0.1685, 0.1685
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Proof_that_e_is_irrational.html
∑
n
=
0
∞
(
-
1
)
n
(
n
+
1
)
(
n
+
2
)
=
2
ln
2
-
1.
Doc 75
0.1644, 0.1644
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
e
=
∑
n
=
0
∞
1
n
!
≈
2.71828
Doc 76
0.1639, 0.1639
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Dimensionless_quantity.html
𝐀
-
1
=
∑
n
=
0
∞
(
𝐈
-
𝐀
)
n
.
Doc 77
0.1604, 0.1604
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Invertible_matrix.html
π
2
sin
2
π
z
=
∑
n
=
-
∞
∞
1
(
z
-
n
)
2
.
Doc 78
0.1596, 0.1596
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sine.html
Φ
(
exp
(
2
π
i
λ
)
,
s
,
α
)
=
L
(
λ
,
α
,
s
)
.
Doc 1
1.0000, 1.9451
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lerch_zeta_function.html
ζ
(
s
)
ζ
(
2
s
)
=
∑
n
=
1
∞
|
μ
(
n
)
|
n
s
Doc 79
0.1538, 0.1538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Square-free_integer.html
∑
n
=
0
∞
a
σ
(
n
)
=
∑
n
=
0
∞
a
n
.
Doc 23
0.2969, 0.4507
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
Z
=
∑
n
=
0
∞
(
8
n
+
1
)
(
1
2
)
n
(
1
4
)
n
(
3
4
)
n
(
n
!
)
3
9
n
Doc 60
0.1901, 0.8291
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
g
(
x
)
=
∑
n
=
1
∞
f
(
n
)
exp
(
2
π
i
n
x
)
Doc 80
0.1510, 0.1510
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Multiplication_theorem.html
Z
=
∑
n
=
0
∞
(
6
n
+
1
)
(
1
2
)
n
3
4
n
(
n
!
)
3
Doc 60
0.1901, 0.8291
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/List_of_formulae_involving_π.html
D
e
D
-
1
=
log
(
Δ
+
1
)
Δ
=
∑
n
=
0
∞
(
-
Δ
)
n
n
+
1
.
Doc 26
0.2867, 0.4200
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_polynomials.html
1
(
1
-
z
)
α
+
1
=
∑
n
=
0
∞
(
n
+
α
n
)
z
n
Doc 81
0.1238, 0.1238
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html