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 ]

Doc 1
1.0000
1.9451
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Lerch_zeta_function.html
L ( λ , α , s ) = n = 0 exp ( 2 π i λ n ) ( n + α ) s .
Φ ( z , s , α ) = n = 0 z n ( n + α ) s .
L ( λ , α , s )
Φ ( exp ( 2 π i λ ) , s , α ) = L ( λ , α , s ) .

Doc 2
0.5579
0.5579
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Catalan's_constant.html
Φ ( z , s , α ) = n = 0 z n ( n + α ) s .

Doc 3
0.4533
0.4533
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Ramanujan's_master_theorem.html
ζ ( s , a ) = n = 0 1 ( n + a ) s

Doc 4
0.4518
1.3635
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Riemann_zeta_function.html
Φ ( z , s , q ) = k = 0 z k ( k + q ) s
ζ ( s , q ) = k = 0 1 ( k + q ) s
log 2 = n = 1 ζ ( 2 n ) - 1 n .
1 ζ ( s ) = n = 1 μ ( n ) n s

Doc 5
0.4518
0.8399
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Hurwitz_zeta_function.html
Φ ( z , s , q ) = k = 0 z k ( k + q ) s
ζ ( s , q ) = n = 0 1 ( q + n ) s .

Doc 6
0.3830
0.3830
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Multiple_zeta_function.html
ζ ( s , t ) = n = 1 H n , t ( n + 1 ) s

Doc 7
0.3744
0.3744
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_L-function.html
L ( s , χ ) = n = 1 χ ( n ) n s .

Doc 8
0.3725
0.3725
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Modularity_theorem.html
L ( E , s ) = 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
L ( s , E ) = n = 1 a n n s .

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
f ( 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
blanc ( x ) = n = 0 s ( 2 n x ) 2 n ,

Doc 12
0.3488
0.5854
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Minakshisundaram–Pleijel_zeta_function.html
Z ( P , Q , s ) = n = 1 f n ( P ) f n ( Q ) λ n s
Z ( s ) = n 0 1 ( n 2 ) s = 2 ζ ( 2 s )

Doc 13
0.3447
0.3447
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Generalized_Riemann_hypothesis.html
L ( χ , s ) = 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
L ( s , χ ) = n = 1 χ ( n ) n s

Doc 15
0.3318
0.3318
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Conway–Maxwell–Poisson_distribution.html
Z ( λ , ν ) = j = 0 λ j ( j ! ) ν .

Doc 16
0.3317
0.6233
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Selberg_class.html
L ( s , Δ ) = n = 1 a n n s
F χ ( s ) = n = 1 χ ( n ) a n n s

Doc 17
0.3150
2.3229
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_series.html
F ( s ) = n = 1 f ( n ) n s
ζ 2 ( s ) = n = 1 d ( n ) n s
ζ ( 2 s ) ζ ( s ) = n = 1 λ ( n ) n s .
ζ 4 ( s ) ζ ( 2 s ) = n = 1 d ( n ) 2 n s .
σ 1 - s ( m ) ζ ( s ) = n = 1 c n ( m ) n s .
1 ζ ( s ) = n = 1 μ ( n ) n s
ζ ( s - 1 ) ζ ( s ) = n = 1 φ ( n ) n s
ζ 3 ( s ) ζ ( 2 s ) = n = 1 d ( n 2 ) n s
ζ ( s - k ) ζ ( s ) = n = 1 J k ( n ) n s
1 L ( χ , s ) = n = 1 μ ( n ) χ ( n ) n s

Doc 18
0.3150
0.3150
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Von_Mangoldt_function.html
F ( s ) = n = 1 f ( n ) n s

Doc 19
0.3150
0.3150
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Perron's_formula.html
g ( 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
φ ( s ) = n = 1 a n n s .

Doc 21
0.3045
0.6036
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Net_present_value.html
NPV ( i , N ) = t = 0 N R t ( 1 + i ) t
NPV ( i ) = t = 0 N R t ( 1 + i ) t

Doc 22
0.3037
0.3037
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Trigamma_function.html
ψ 1 ( z ) = n = 0 1 ( z + n ) 2 ,

Doc 23
0.2969
0.4507
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Series_(mathematics).html
ζ ( s ) = n = 1 1 n s .
n = 0 a σ ( n ) = n = 0 a n .

Doc 24
0.2969
0.2969
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/List_of_zeta_functions.html
ζ ( s ) = n = 1 1 n s .

Doc 25
0.2969
0.2969
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Basel_problem.html
ζ ( s ) = n = 1 1 n s .

Doc 26
0.2867
0.4200
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Bernoulli_polynomials.html
S ν ( x ) = k = 0 sin ( ( 2 k + 1 ) π x ) ( 2 k + 1 ) ν
D e D - 1 = log ( Δ + 1 ) Δ = n = 0 ( - Δ ) n n + 1 .

Doc 27
0.2864
0.5364
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Functional_determinant.html
ζ S ( s ) = n = 1 1 λ n s .
n = 0 1 ( n + a )

Doc 28
0.2804
0.2804
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Stieltjes_transformation.html
S ρ ( z ) = n = 0 m n z n + 1 .

Doc 29
0.2778
0.5542
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/P-adic_exponential_function.html
exp ( z ) = n = 0 z n n ! .
exp p ( z ) = n = 0 z n n ! .

Doc 30
0.2677
0.2677
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Engel_expansion.html
1 n = r = 1 1 ( n + 1 ) r .

Doc 31
0.2634
0.2634
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Dirichlet_convolution.html
D G ( f ; s ) = n = 1 f ( n ) n s

Doc 32
0.2632
0.4912
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Nachbin's_theorem.html
F ( w ) = n = 0 f n Ψ n w n + 1 .
f ( x ) = n = 0 a n M ( n + 1 ) x n

Doc 33
0.2614
0.2614
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Dirichlet_beta_function.html
β ( s ) = n = 0 ( - 1 ) n ( 2 n + 1 ) s ,

Doc 34
0.2609
0.2609
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Zipf–Mandelbrot_law.html
H N , q , s = i = 1 N 1 ( i + q ) s

Doc 35
0.2531
0.2531
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Portal:Infrastructure::Economic_analysis.html
N P V = n = 0 N C n ( 1 + r ) n = 0

Doc 36
0.2513
0.2513
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Q-analog.html
e q x = n = 0 x n [ n ] q ! .

Doc 37
0.2427
0.2427
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Internal_rate_of_return.html
NPV = n = 0 N C n ( 1 + r ) n = 0

Doc 38
0.2419
0.2419
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Sophomore's_dream.html
x x = exp ( x log x ) = n = 0 x n ( log x ) n n ! .

Doc 39
0.2405
0.2405
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Polymer_field_theory.html
Ξ ( μ , V , β ) = n = 0 e β μ n Z ( n , V , β ) ,

Doc 40
0.2402
0.2402
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Skew-symmetric_matrix.html
R = exp ( A ) = n = 0 A n n ! .

Doc 41
0.2371
0.2371
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sine-Gordon_equation.html
cos ( φ ) = n = 0 ( - φ 2 ) n ( 2 n ) ! ,

Doc 42
0.2358
0.2358
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Gauss–Kuzmin–Wirsing_operator.html
t n = m = 0 G m n ( m + 1 ) ( m + 2 ) .

Doc 43
0.2350
0.2350
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Compound_Poisson_process.html
exp ( ν ) = n = 0 ν * n n !

Doc 44
0.2346
0.2346
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Mortgage_yield.html
Mortgage Yield: ri such that P = n = 1 N C ( t ) ( 1 + r i / 1200 ) t - 1

Doc 45
0.2341
0.2341
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Liouville_function.html
ζ ( 2 s ) ζ ( s ) = n = 1 λ ( n ) n s .

Doc 46
0.2308
0.4222
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Generating_function.html
DG ( a n ; s ) = n = 1 a n n s .
e x f ( t ) = n = 0 p n ( x ) n ! t n

Doc 47
0.2302
0.2302
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Shimizu_L-function.html
L ( M , V , s ) = μ { M - 0 } / V sign N ( μ ) | N ( μ ) | s

Doc 48
0.2281
0.2281
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Integral_equation.html
f ( t ) = n = 0 a n M ( n + 1 ) x n

Doc 49
0.2275
0.4234
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hyperbolic_angle.html
cosh x = n = 0 x 2 n ( 2 n ) !
sinh x = n = 0 x 2 n + 1 ( 2 n + 1 ) !

Doc 50
0.2233
0.2233
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Rate_of_return.html
NPV = t = 0 n C t ( 1 + r ) t = 0

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
1 ζ ( s ) = n = 1 μ ( n ) n s ,

Doc 53
0.2132
0.2132
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Converse_theorem.html
L χ ( s ) = χ ( n ) a n n s

Doc 54
0.2131
0.2131
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000014/Articles/Hermite's_problem.html
x = n = 0 a n 10 n .

Doc 55
0.2120
0.2120
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Factorial.html
e x = n = 0 x n n ! .

Doc 56
0.2120
0.2120
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Auxiliary_function.html
e x = n = 0 x n n ! .

Doc 57
0.2079
0.2079
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Formal_power_series.html
( 1 - X ) - 1 = n = 0 X n .

Doc 58
0.2048
0.2048
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Q-Pochhammer_symbol.html
1 ( x ; q ) = n = 0 x n ( q ; q ) n

Doc 59
0.2047
0.2047
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Completely_multiplicative_function.html
L ( s , a ) = n = 1 a ( n ) n s = p ( 1 - a ( p ) p s ) - 1 ,

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 ( ( 2 n ) ! ) 3 ( 42 n + 5 ) ( n ! ) 6 16 3 n + 1
Z = n = 0 ( - 1 ) n ( 4 n ) ! ( 21460 n + 1123 ) ( n ! ) 4 4 4 n 882 2 n
Z = n = 0 ( - 1 ) n ( 4 n ) ! ( 260 n + 23 ) ( n ! ) 4 4 4 n 18 2 n
Z = n = 0 ( 8 n + 1 ) ( 1 2 ) n ( 1 4 ) n ( 3 4 ) n ( n ! ) 3 9 n
Z = n = 0 ( 6 n + 1 ) ( 1 2 ) n 3 4 n ( n ! ) 3

Doc 61
0.1895
0.1895
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Erdős–Borwein_constant.html
E = n = 1 σ 0 ( n ) 2 n

Doc 62
0.1856
0.1856
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Telescoping_series.html
n = 0 2 n + 3 ( n + 1 ) ( n + 2 )

Doc 63
0.1833
0.1833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Exponentiation.html
e x = n = 0 x n n !

Doc 64
0.1833
0.1833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Frequency_mixer.html
e x = n = 0 x n n !

Doc 65
0.1833
0.1833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Real_number.html
e x = n = 0 x n n !

Doc 66
0.1833
0.1833
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Exponential_function.html
e z = n = 0 z n n !

Doc 67
0.1826
0.1826
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Digamma_function.html
n = 0 u n = n = 0 p ( n ) q ( n ) ,

Doc 68
0.1812
0.1812
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Quadratic_Gauss_sum.html
G ( a , 0 , c ) = n = 0 c - 1 ( n c ) e 2 π i a n / c .

Doc 69
0.1781
0.1781
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Square_root_of_2.html
1 2 = k = 0 ( - 1 ) k ( π 4 ) 2 k ( 2 k ) ! .

Doc 70
0.1776
0.1776
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Eulerian_number.html
e 1 - e x = n = 0 A n ( x ) n ! ( 1 - x ) n + 1 .

Doc 71
0.1724
0.1724
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/E_(mathematical_constant).html
e = n = 0 1 n !

Doc 72
0.1705
0.1705
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Asymptotic_expansion.html
1 1 - w = n = 0 w n .

Doc 73
0.1703
0.1703
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Baker–Campbell–Hausdorff_formula.html
exp X = e X = n = 0 X n n ! .

Doc 74
0.1685
0.1685
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Proof_that_e_is_irrational.html
e = n = 0 1 n !

Doc 75
0.1644
0.1644
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
n = 0 ( - 1 ) n ( n + 1 ) ( n + 2 ) = 2 ln 2 - 1.

Doc 76
0.1639
0.1639
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Dimensionless_quantity.html
e = n = 0 1 n ! 2.71828

Doc 77
0.1604
0.1604
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Invertible_matrix.html
𝐀 - 1 = n = 0 ( 𝐈 - 𝐀 ) n .

Doc 78
0.1596
0.1596
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sine.html
π 2 sin 2 π z = n = - 1 ( z - n ) 2 .

Doc 79
0.1538
0.1538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Square-free_integer.html
ζ ( s ) ζ ( 2 s ) = n = 1 | μ ( n ) | n s

Doc 80
0.1510
0.1510
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Multiplication_theorem.html
g ( x ) = n = 1 f ( n ) exp ( 2 π i n x )

Doc 81
0.1238
0.1238
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