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 ]

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 ( 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
0.6651
-3.0000
11.0000
1.3120
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
0.6651
-3.0000
11.0000
1.2121
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
0.6651
-4.0000
11.0000
0.6651
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
0.6468
-1.0000
9.0000
0.6468
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 6
0.6468
-4.0000
8.0000
1.0974
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 7
0.6429
-7.0000
10.0000
0.6429
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 8
0.6258
-8.0000
9.0000
0.6258
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 9
0.5864
-3.0000
8.0000
1.1334
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 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
f ( x ) = n = 0 s ( 2 n x ) 2 n
f ( x ) = k = 1 sin ( 2 k x ) 2 k

Doc 11
0.5470
-2.0000
8.0000
0.5470
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Generalized_Riemann_hypothesis.html
L ( χ , s ) = 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 ( 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
L ( s , χ ) = n = 1 χ ( n ) n s .
n = 1 k χ ( n ) exp ( 2 π i n / k ) .

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
Z ( λ , ν ) = j = 0 λ j ( j ! ) ν .

Doc 15
0.5470
-3.0000
8.0000
0.5470
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Blancmange_curve.html
blanc ( x ) = n = 0 s ( 2 n x ) 2 n ,

Doc 16
0.5470
-7.0000
8.0000
0.5470
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 17
0.5470
-14.0000
8.0000
0.5470
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 18
0.5470
-19.0000
9.0000
0.5470
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 19
0.5291
-17.0000
8.0000
0.5291
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 20
0.5240
-14.0000
7.0000
0.5240
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 21
0.5076
-2.0000
7.0000
0.5076
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Selberg_class.html
L ( s , Δ ) = 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 ( E , s ) = 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
L ( s , E ) = n = 1 a n n s .

Doc 24
0.5076
-4.0000
8.0000
0.5076
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Trigamma_function.html
ψ 1 ( z ) = n = 0 1 ( z + n ) 2 ,

Doc 25
0.5076
-5.0000
8.0000
0.9391
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 26
0.5076
-6.0000
8.0000
0.5076
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 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
f ( x ) = k = 1 sin ( 2 k x ) 2 k

Doc 28
0.4898
-7.0000
7.0000
0.4898
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 29
0.4898
-9.0000
7.0000
0.4898
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 30
0.4898
-15.0000
7.0000
0.4898
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 31
0.4681
-3.0000
7.0000
0.4681
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 32
0.4681
-13.0000
7.0000
0.9186
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Gauss–Kuzmin–Wirsing_operator.html
[ G f ] ( x ) = n = 1 1 ( x + n ) 2 f ( 1 x + n ) .
t n = m = 0 G m n ( m + 1 ) ( m + 2 ) .

Doc 33
0.4505
-7.0000
6.0000
0.4505
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 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 2 ( n + 1 ) 2 = 11 360 π 4 ;

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
P V = t = 1 n F V t ( 1 + i ) 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
D P V = t = 0 N F V t ( 1 + r ) t

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
N P V = n = 0 N C n ( 1 + r ) n = 0

Doc 38
0.4444
-11.0000
7.0000
0.4444
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 39
0.4444
-14.0000
7.0000
0.4444
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 40
0.4444
-19.0000
7.0000
0.4444
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 41
0.4286
-1.0000
6.0000
0.4286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Closed-form_expression.html
f ( x ) = i = 0 x 2 i

Doc 42
0.4286
-4.0000
6.0000
0.4286
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 43
0.4286
-5.0000
7.0000
0.4286
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 44
0.4286
-5.0000
7.0000
0.4286
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 45
0.4286
-5.0000
6.0000
0.4286
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000011/Articles/Distributed_lag.html
w i = j = 2 n a j ( i + 1 ) j ,

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 ( ( 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 47
0.4045
-7.0000
8.0000
0.7286
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 48
0.3890
-6.0000
7.0000
0.3890
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Engel_expansion.html
1 n = r = 1 1 ( n + 1 ) r .

Doc 49
0.3890
-8.0000
7.0000
0.3890
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Sine-Gordon_equation.html
cos ( φ ) = n = 0 ( - φ 2 ) n ( 2 n ) ! ,

Doc 50
0.3719
-1.0000
7.0000
0.3719
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Functional_determinant.html
n = 0 1 ( n + a )

Doc 51
0.3719
-4.0000
4.0000
0.3719
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Refinable_function.html
φ ( x ) = i s i ( x - i ) k

Doc 52
0.3719
-8.0000
7.0000
0.3719
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Telescoping_series.html
n = 0 2 n + 3 ( n + 1 ) ( n + 2 )

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
ϑ 00 ( z , q ) = n = - q n 2 exp ( 2 π i n z )
ϑ 0 , 0 ( x ) = n = - q n 2 exp ( 2 π i n x / a )

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
n = 0 ( - 1 ) n ( n + 1 ) ( n + 2 ) = 2 ln 2 - 1.
n = 1 ( - 1 ) n + 1 n = n = 0 1 ( 2 n + 1 ) ( 2 n + 2 ) = ln 2.

Doc 55
0.3644
-4.0000
6.0000
0.3644
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Compound_interest.html
L = P j = 1 n 1 ( 1 + i ) j

Doc 56
0.3493
-4.0000
6.0000
0.3493
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Geometric_series.html
n = 1 $ 100 ( 1 + I ) n ,

Doc 57
0.3493
-5.0000
7.0000
0.3493
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Polygamma_function.html
k = 0 ( - 1 ) k ( z + k ) m + 1

Doc 58
0.3493
-5.0000
5.0000
0.3493
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 59
0.3493
-5.0000
5.0000
0.3493
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 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
e = k = 0 3 - 4 k 2 ( 2 k + 1 ) !
e = k = 0 ( 3 k ) 2 + 1 ( 3 k ) !

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 z 2 k + 1 ( 2 k + 1 ) ! = sinh z
k = 0 ( - 1 ) k z 2 k + 1 ( 2 k + 1 ) ! = sin z

Doc 62
0.3493
-9.0000
7.0000
0.3493
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 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
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 64
0.3493
-16.0000
8.0000
0.3493
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 65
0.3326
-10.0000
4.0000
0.3326
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 66
0.3326
-10.0000
3.0000
0.3326
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 67
0.3326
-14.0000
5.0000
0.5863
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Theta_function.html
θ ^ F ( z ) = k = 0 R F ( k ) exp ( 2 π i k z ) ,
θ F ( z ) = m Z n exp ( 2 π i z F ( m ) )

Doc 68
0.3241
-6.0000
6.0000
0.3241
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000010/Articles/Golomb–Dickman_constant.html
λ = 0 ρ ( t ) ( t + 1 ) 2 d t

Doc 69
0.3096
-3.0000
6.0000
0.3096
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Decimal_representation.html
r = i = 0 a i 10 i

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
τ = i = 0 t i 2 i + 1

Doc 71
0.3096
-10.0000
7.0000
0.5792
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
0.2932
-14.0000
5.0000
0.2932
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 73
0.2932
-15.0000
6.0000
0.2932
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 74
0.2835
-16.0000
8.0000
0.2835
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 75
0.2697
-12.0000
6.0000
0.2697
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000007/Articles/Sine.html
π 2 sin 2 π z = n = - 1 ( z - n ) 2 .

Doc 76
0.2538
-2.0000
5.0000
0.2538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Volume_conjecture.html
q = exp ( 2 π i / N )

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
z = exp ( 2 π i / 3 ) .

Doc 78
0.2538
-7.0000
5.0000
0.2538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Ivan_Matveyevich_Vinogradov.html
S = p P exp ( 2 π i f ( p ) ) .

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
1 sin 2 ( z ) = n 1 ( z - n π ) 2

Doc 80
0.2143
-16.0000
5.0000
0.4286
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

Doc 81
0.2143
-16.0000
3.0000
0.2143
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 .