Returned 94 matches (100 formulae, 81 docs)
    Lookup 434.350 ms, Re-ranking 4711.915 ms
    Found 1285716 tuple postings, 226251 formulae, 23811 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
0.9817
1.8443
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 .
Φ ( z , s , a ) = z n Φ ( z , s , a + n ) + k = 0 n - 1 z k ( k + a ) s
Φ ( exp ( 2 π i λ ) , s , α ) = L ( λ , α , s ) .

Doc 2
0.4843
0.8575
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

Doc 3
0.4843
0.8021
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 4
0.4737
0.4737
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 5
0.3746
0.3746
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 6
0.3732
0.3732
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 7
0.3391
0.3391
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 8
0.3158
0.3158
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Trigamma_function.html
ψ 1 ( z ) = n = 0 1 ( z + n ) 2 ,

Doc 9
0.3109
0.3109
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Engel_expansion.html
1 n = r = 1 1 ( n + 1 ) r .

Doc 10
0.3088
0.3088
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

Doc 11
0.3085
0.3085
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 12
0.3085
0.3085
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 13
0.3084
0.4747
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Clausen_function.html
β ( x ) = k = 0 ( - 1 ) k ( 2 k + 1 ) x
Cl 2 m ( q π p ) = k = 1 sin ( k q π / p ) k 2 m

Doc 14
0.3069
0.3069
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 15
0.3025
0.3025
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 16
0.2985
0.2985
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Rational_pricing.html
P 0 = t = 1 T C t ( 1 + r t ) t

Doc 17
0.2985
0.2985
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Generalized_Riemann_hypothesis.html
L ( χ , s ) = n = 1 χ ( n ) n s

Doc 18
0.2985
0.2985
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Dirichlet_character.html
L ( s , χ ) = n = 1 χ ( n ) n s

Doc 19
0.2977
0.5943
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 20
0.2957
0.5168
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
n = 1 H ¯ n ( b ) ( n + 1 ) a = ζ ( a , b ¯ )

Doc 21
0.2946
0.5202
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 ) .
[ G f ] ( x ) = n = 1 1 ( x + n ) 2 f ( 1 x + n ) .

Doc 22
0.2913
0.5255
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dirichlet_L-function.html
L ( s , χ ) = n = 1 χ ( n ) n s .
n = 1 k χ ( n ) exp ( 2 π i n / k ) .

Doc 23
0.2894
0.2894
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Legendre_chi_function.html
χ ν ( z ) = k = 0 z 2 k + 1 ( 2 k + 1 ) ν .

Doc 24
0.2893
0.2893
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Functional_determinant.html
n = 0 1 ( n + a )

Doc 25
0.2846
0.2846
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

Doc 26
0.2843
0.2843
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Distributed_lag.html
w i = j = 2 n a j ( i + 1 ) j ,

Doc 27
0.2842
0.4726
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/List_of_representations_of_e.html
e = k = 0 3 - 4 k 2 ( 2 k + 1 ) !
e = k = 0 ( 3 k ) 2 + 1 ( 3 k ) !

Doc 28
0.2799
0.2799
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Wright_Omega_function.html
ω ( z ) = n = 0 + q n ( ω a ) ( 1 + ω a ) 2 n - 1 ( z - a ) n n !

Doc 29
0.2786
0.2786
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Compound_interest.html
L = P j = 1 n 1 ( 1 + i ) j

Doc 30
0.2742
0.2742
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Polygamma_function.html
k = 0 ( - 1 ) k ( z + k ) m + 1

Doc 31
0.2699
0.2699
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Holding_value.html
H V [ i , n ] = k = 0 n - i d i v ( i + k ) ( 1 + r ) n - i - k

Doc 32
0.2684
0.2684
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Discounted_cash_flow.html
D P V = t = 0 N F V t ( 1 + r ) t

Doc 33
0.2680
0.2680
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Selberg_class.html
L ( s , Δ ) = n = 1 a n n s

Doc 34
0.2644
0.4535
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Hyperbolic_angle.html
sinh x = n = 0 x 2 n + 1 ( 2 n + 1 ) !
cosh x = n = 0 x 2 n ( 2 n ) !

Doc 35
0.2627
0.2627
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
0.2622
0.2622
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/Sobolev_spaces_for_planar_domains.html
λ n = m ( 1 + n 2 ) k - 1 2 ( 1 + m 2 + n 2 ) k .

Doc 37
0.2617
0.2617
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Time_value_of_money.html
P V = t = 1 n F V t ( 1 + i ) t

Doc 38
0.2613
0.2613
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Modularity_theorem.html
L ( E , s ) = n = 1 a n n s .

Doc 39
0.2613
0.2613
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Modular_elliptic_curve.html
L ( s , E ) = n = 1 a n n s .

Doc 40
0.2573
0.2573
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Volume_conjecture.html
q = exp ( 2 π i / N )

Doc 41
0.2515
0.2515
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Geometric_series.html
n = 1 $ 100 ( 1 + I ) n ,

Doc 42
0.2514
0.2514
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Butson-type_Hadamard_matrix.html
z = exp ( 2 π i / 3 ) .

Doc 43
0.2434
0.2434
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Telescoping_series.html
n = 0 2 n + 3 ( n + 1 ) ( n + 2 )

Doc 44
0.2420
0.2420
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Invariant_basis_number.html
f ( i 1 , , i n ) = k = 0 n i k f ( e k ) I p

Doc 45
0.2418
0.2418
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 46
0.2370
0.4305
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
f ( x ) = k = 1 sin ( 2 k x ) 2 k

Doc 47
0.2359
0.2359
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Harmonic_number.html
n = 1 H n 2 ( n + 1 ) 2 = 11 360 π 4 ;

Doc 48
0.2323
0.2323
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Ivan_Matveyevich_Vinogradov.html
S = p P exp ( 2 π i f ( p ) ) .

Doc 49
0.2315
0.2315
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Blancmange_curve.html
blanc ( x ) = n = 0 s ( 2 n x ) 2 n ,

Doc 50
0.2302
0.2302
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Crenel_function.html
P m ( Δ , x ) = exp ( 2 π i m x ) sin ( π m Δ ) π m .

Doc 51
0.2284
0.4341
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000008/Articles/Partial_fractions_in_complex_analysis.html
k = 0 1 ( 2 k + 1 ) 2 = π 2 2 3 = π 2 8
k = 0 1 ( 2 k + 1 ) 4 = 1 3 π 4 2 5 = π 4 96 .

Doc 52
0.2251
0.5878
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
Doc 53
0.2247
0.3972
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Theta_function.html
θ F ( z ) = m Z n exp ( 2 π i z F ( m ) )
θ ^ F ( z ) = k = 0 R F ( k ) exp ( 2 π i k z ) ,

Doc 54
0.2222
0.2222
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Golomb–Dickman_constant.html
λ = 0 ρ ( t ) ( t + 1 ) 2 d t

Doc 55
0.2221
0.2221
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Q-derivative.html
D q ( f ( x ) ) = k = 0 ( q - 1 ) k ( k + 1 ) ! x k f ( k + 1 ) ( x ) .

Doc 56
0.2220
0.2220
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Hua's_lemma.html
f ( α ) = x = 1 N exp ( 2 π i P ( x ) α ) ,

Doc 57
0.2220
0.4369
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Natural_logarithm_of_2.html
n = 1 ( - 1 ) n + 1 n = n = 0 1 ( 2 n + 1 ) ( 2 n + 2 ) = ln 2.
n = 0 ( - 1 ) n ( n + 1 ) ( n + 2 ) = 2 ln 2 - 1.

Doc 58
0.2218
0.2218
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Confluent_hypergeometric_function.html
M ( a , b , z ) = n = 0 a ( n ) z n b ( n ) n ! = F 1 1 ( a ; b ; z ) ,

Doc 59
0.2214
0.2214
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Present_value.html
P V = k = 1 C ( 1 + i ) k = C i , i > 0 ,

Doc 60
0.2211
0.4273
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/List_of_mathematical_series.html
k = 0 z 2 k + 1 ( 2 k + 1 ) ! = sinh z
k = 0 ( - 1 ) k z 2 k + 1 ( 2 k + 1 ) ! = sin z

Doc 61
0.2191
0.2191
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Dividend_discount_model.html
P = t = 1 N D 0 ( 1 + g ) t ( 1 + r ) t + P N ( 1 + r ) N

Doc 62
0.2185
0.2185
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Stirling's_approximation.html
0 2 arctan ( t x ) e 2 π t - 1 d t = n = 1 c n ( x + 1 ) n ¯

Doc 63
0.2173
0.2173
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Sinc_function.html
sinc ( x ) = sin ( x ) x = n = 0 ( - x 2 ) n ( 2 n + 1 ) !

Doc 64
0.2141
0.2141
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Apéry's_constant.html
ζ ( 3 ) = 8 7 k = 0 1 ( 2 k + 1 ) 3

Doc 65
0.2126
0.2126
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000015/Articles/List_of_OEIS_sequences.html
τ = i = 0 t i 2 i + 1

Doc 66
0.2101
0.2101
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sine.html
π 2 sin 2 π z = n = - 1 ( z - n ) 2 .

Doc 67
0.2069
0.2069
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Decimal_representation.html
r = i = 0 a i 10 i

Doc 68
0.2055
0.2055
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Chinese_remainder_theorem.html
1 Q = i = 1 r S i ( x - λ i ) ν i

Doc 69
0.2055
0.2055
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Partial_fraction_decomposition.html
P Q = j = 1 r A j ( x - λ j ) ν j

Doc 70
0.2042
0.3824
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Jacobi_theta_functions_(notational_variations).html
ϑ 0 , 0 ( x ) = n = - q n 2 exp ( 2 π i n x / a )
ϑ 00 ( z , q ) = n = - q n 2 exp ( 2 π i n z )

Doc 71
0.2022
0.3754
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Q-Pochhammer_symbol.html
1 ( x ; q ) = n = 0 x n ( q ; q ) n
( a x ; q ) ( x ; q ) = n = 0 ( a ; q ) n ( q ; q ) n x n .

Doc 72
0.1978
0.1978
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Closed-form_expression.html
f ( x ) = i = 0 x 2 i

Doc 73
0.1935
0.1935
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/List_of_fractals_by_Hausdorff_dimension.html
f ( x ) = k = 1 sin ( 2 k x ) 2 k

Doc 74
0.1915
0.1915
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 75
0.1898
0.1898
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 76
0.1833
0.1833
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 77
0.1824
0.1824
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Mittag-Leffler's_theorem.html
1 sin 2 ( z ) = n 1 ( z - n π ) 2

Doc 78
0.1741
0.1741
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sine-Gordon_equation.html
cos ( φ ) = n = 0 ( - φ 2 ) n ( 2 n ) ! ,

Doc 79
0.1715
0.1715
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Refinable_function.html
φ ( x ) = i s i ( x - i ) k

Doc 80
0.1590
0.1590
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Gegenbauer_polynomials.html
1 ( 1 - 2 x t + t 2 ) α = n = 0 C n ( α ) ( x ) t n .

Doc 81
0.1294
0.2562
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html
x l ( 1 - x ) l + 1 = p = 0 ( p l ) x p .
1 ( 1 - z ) α + 1 = n = 0 ( n + α n ) z n