Returned 32 matches (40 formulae, 24 docs)
    Lookup 0.311 ms, Re-ranking 0.086 ms
    Found 42 tuple postings, 40 formulae, 24 documents
[ formulas ] [ documents ] [ documents-by-formula ]

- 0.026838601
Doc 1
1.0000, 2.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Prime_zeta_function.html
- 0.060607633
Doc 1
1.0000, 2.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Prime_zeta_function.html
- 0.150757555
Doc 1
1.0000, 2.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Prime_zeta_function.html
- 0.493091109
Doc 1
1.0000, 2.0000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Prime_zeta_function.html
x = - 1.84208
Doc 2
0.1538, 0.1538
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Quintic_function.html
- 2 5 = - 1.148698354
Doc 3
0.1176, 0.1176
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Nth_root.html
e π 58 = 396 4 - 104.000000177 .
Doc 4
0.0606, 0.0606
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Srinivasa_Ramanujan.html
1393 - 985 2 = - 0.00035
Doc 5
0.0571, 0.3429
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Pell_number.html
1 - 1 2 = - 0.41421
Doc 5
0.0571, 0.3429
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Pell_number.html
239 - 169 2 = - 0.00209
Doc 5
0.0571, 0.3429
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Pell_number.html
41 - 29 2 = - 0.01219
Doc 5
0.0571, 0.3429
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Pell_number.html
7 - 5 2 = - 0.07106
Doc 5
0.0571, 0.3429
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Pell_number.html
8119 - 5741 2 = - 0.00006
Doc 5
0.0571, 0.3429
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Pell_number.html
ϕ 1 = - 30 + 30
Doc 6
0.0556, 0.0556
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000013/Articles/Vienna_rectifier.html
z 1 = - 0.4121345 + i 0.5978119
Doc 7
0.0500, 0.1000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Trigamma_function.html
z 2 = - 1.4455692 + i 0.6992608
Doc 7
0.0500, 0.1000
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Trigamma_function.html
lim k c 2 ( k ) = - 2.157782996659 .
Doc 8
0.0476, 0.0476
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000012/Articles/Spiral_of_Theodorus.html
φ = 1 - 5 2 = - 0.6180 339887
Doc 9
0.0444, 0.0597
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Golden_ratio.html
ζ ( - 1 ) = 1 12 - ln A - 0.1654211437
Doc 10
0.0278, 0.0510
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Particular_values_of_Riemann_zeta_function.html
ϵ n = ϵ - K p . . ( 16 )
Doc 11
0.0267, 0.0267
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000002/Articles/Field_electron_emission.html
ζ ( 0 ) = - 1 2 ln ( 2 π ) - 0.918938533
Doc 10
0.0278, 0.0510
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Particular_values_of_Riemann_zeta_function.html
( π + 20 ) i = - 0.9999999992 - i 0.000039 - 1
Doc 12
0.0227, 0.0227
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Mathematical_coincidence.html
{ 0 , i , i - 1 , - i , i - 1 , - i }
Doc 13
0.0220, 0.0220
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000009/Articles/Misiurewicz_point.html
j 2 A ( - 58 2 ) = 396 4 , e π 58 396 4 - 104.00000017
Doc 14
0.0180, 0.0180
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Dedekind_eta_function.html
- 1 φ = 1 - φ = 1 - 5 2 = - 0.61803 39887 .
Doc 9
0.0444, 0.0597
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Golden_ratio.html
Total resources available = Resources at start of innings - Resources lost by first interruption - Resources lost by second interruption - Resources lost by third interruption - etc
Doc 15
0.0152, 0.0152
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Duckworth–Lewis_method.html
ζ ( 2 ) = Derivative of ζ ( 2 ) = - n = 2 ln n n 2 = - 0.9375482543
Doc 16
0.0123, 0.0123
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000016/Articles/Mathematical_constants_and_functions.html
γ 1 ( 1 2 ) = - 2 γ ln 2 - ln 2 2 + γ 1 = - 1.353459680
Doc 17
0.0117, 0.0133
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Stieltjes_constants.html
θ ( 0 ) = - ln π + γ + π / 2 + 3 ln 2 2 = - 2.6860917
Doc 18
0.0116, 0.0116
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Riemann–Siegel_theta_function.html
c 2 = - 1 6 ; c 3 = - 1 108 ; c 4 = 7 3240 ; c 5 = - 19 48600
Doc 19
0.0068, 0.0068
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Power_series_solution_of_differential_equations.html
H ( X 1 , , X n ) = - x 1 x n P ( x 1 , , x n ) log 2 [ P ( x 1 , , x n ) ]
Doc 20
0.0063, 0.0063
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000004/Articles/Joint_entropy.html
e π 19 ( 5 x ) 3 - 6.000 010 e π 43 ( 5 x ) 3 - 6.000 000 010 e π 67 ( 5 x ) 3 - 6.000 000 000 061 e π 163 ( 5 x ) 3 - 6.000 000 000 000 000 034
Doc 21
0.0063, 0.0121
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Heegner_number.html
M = - 6 + 12 / 2 - 8 / 3 + 6 / 2 - 24 / 5 + = - 1.74756 .
Doc 22
0.0051, 0.0051
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000006/Articles/Madelung_constant.html
e π 163 = ( e π i / 24 η ( τ ) η ( 2 τ ) ) 24 - 24.000 000 000 000 001 05 e π 163 = ( e π i / 12 η ( τ ) η ( 3 τ ) ) 12 - 12.000 000 000 000 000 21 e π 163 = ( e π i / 6 η ( τ ) η ( 5 τ ) ) 6 - 6.000 000 000 000 000 034
Doc 21
0.0063, 0.0121
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Heegner_number.html
( - n k ) = - n - ( n + 1 ) - ( n + k - 2 ) - ( n + k - 1 ) k ! = ( - 1 ) k n ( n + 1 ) ( n + 2 ) ( n + k - 1 ) k ! = ( - 1 ) k ( n + k - 1 k ) = ( - 1 ) k ( ( n k ) ) .
Doc 23
0.0025, 0.0025
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000001/Articles/Binomial_coefficient.html
1 , 1 , 2 , 3 , 1 , - 2 , - 3 , - 5 , - 2 , - 3 , for the signs + , + , + , - , - , + , - , - , .
Doc 24
0.0020, 0.0020
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Random_Fibonacci_sequence.html
e π 19 3 5 ( 3 - 2 ( - 3 + 1 3 19 ) ) - 2 - 12.000 06 e π 43 3 5 ( 9 - 2 ( - 39 + 7 3 43 ) ) - 2 - 12.000 000 061 e π 67 3 5 ( 21 - 2 ( - 219 + 31 3 67 ) ) - 2 - 12.000 000 000 36 e π 163 3 5 ( 231 - 2 ( - 26 679 + 2 413 3 163 ) ) - 2 - 12.000 000 000 000 000 21
Doc 21
0.0063, 0.0121
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000003/Articles/Heegner_number.html
γ 1 ( 1 4 ) = 2 π ln Γ ( 1 4 ) - 3 π 2 ln π - 7 2 ln 2 2 - ( 3 γ + 2 π ) ln 2 - γ π 2 + γ 1 = - 5.518076350 γ 1 ( 3 4 ) = - 2 π ln Γ ( 1 4 ) + 3 π 2 ln π - 7 2 ln 2 2 - ( 3 γ - 2 π ) ln 2 + γ π 2 + γ 1 = - 0.3912989024 γ 1 ( 1 3 ) = - 3 γ 2 ln 3 - 3 4 ln 2 3 + π 4 3 { ln 3 - 8 ln 2 π - 2 γ + 12 ln Γ ( 1 3 ) } + γ 1 = - 3.259557515
Doc 17
0.0117, 0.0133
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Stieltjes_constants.html
γ 1 ( 2 3 ) = - 3 γ 2 ln 3 - 3 4 ln 2 3 - π 4 3 { ln 3 - 8 ln 2 π - 2 γ + 12 ln Γ ( 1 3 ) } + γ 1 = - 0.5989062842 γ 1 ( 1 6 ) = - 3 γ 2 ln 3 - 3 4 ln 2 3 - ln 2 2 - ( 3 ln 3 + 2 γ ) ln 2 + 3 π 3 2 ln Γ ( 1 6 ) - π 2 3 { 3 ln 3 + 11 ln 2 + 15 2 ln π + 3 γ } + γ 1 = - 10.74258252 γ 1 ( 5 6 ) = - 3 γ 2 ln 3 - 3 4 ln 2 3 - ln 2 2 - ( 3 ln 3 + 2 γ ) ln 2 - 3 π 3 2 ln Γ ( 1 6 ) + π 2 3 { 3 ln 3 + 11 ln 2 + 15 2 ln π + 3 γ } + γ 1 = - 0.2461690038
Doc 17
0.0117, 0.0133
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Stieltjes_constants.html
γ 1 ( 1 5 ) = γ 1 + 5 2 { ζ ′′ ( 0 , 1 5 ) + ζ ′′ ( 0 , 4 5 ) } + π 10 + 2 5 2 ln Γ ( 1 5 ) + π 10 - 2 5 2 ln Γ ( 2 5 ) + { 5 2 ln 2 - 5 2 ln ( 1 + 5 ) - 5 4 ln 5 - π 25 + 10 5 10 } γ - 5 2 { ln 2 + ln 5 + ln π + π 25 - 10 5 10 } ln ( 1 + 5 ) + 5 2 ln 2 2 + 5 ( 1 - 5 ) 8 ln 2 5 + 3 5 4 ln 2 ln 5 + 5 2 ln 2 ln π + 5 4 ln 5 ln π - π ( 2 25 + 10 5 + 5 25 + 2 5 ) 20 ln 2 - π ( 4 25 + 10 5 - 5 5 + 2 5 ) 40 ln 5 - π ( 5 5 + 2 5 + 25 + 10 5 ) 10 ln π = - 8.030205511 γ 1 ( 1 8 ) = γ 1 + 2 { ζ ′′ ( 0 , 1 8 ) + ζ ′′ ( 0 , 7 8 ) } + 2 π 2 ln Γ ( 1 8 ) - π 2 ( 1 - 2 ) ln Γ ( 1 4 ) - { 1 + 2 2 π + 4 ln 2 + 2 ln ( 1 + 2 ) } γ - 1 2 ( π + 8 ln 2 + 2 ln π ) ln ( 1 + 2 ) - 7 ( 4 - 2 ) 4 ln 2 2 + 1 2 ln 2 ln π - π ( 10 + 11 2 ) 4 ln 2 - π ( 3 + 2 2 ) 2 ln π = - 16.64171976 γ 1 ( 1 12 ) = γ 1 + 3 { ζ ′′ ( 0 , 1 12 ) + ζ ′′ ( 0 , 11 12 ) } + 4 π ln Γ ( 1 4 ) + 3 π 3 ln Γ ( 1 3 ) - { 2 + 3 2 π + 3 2 ln 3 - 3 ( 1 - 3 ) ln 2 + 2 3 ln ( 1 + 3 ) } γ - 2 3 ( 3 ln 2 + ln 3 + ln π ) ln ( 1 + 3 ) - 7 - 6 3 2 ln 2 2 - 3 4 ln 2 3 + 3 3 ( 1 - 3 ) 2 ln 3 ln 2 + 3 ln 2 ln π - π ( 17 + 8 3 ) 2 3 ln 2 + π ( 1 - 3 ) 3 4 ln 3 - π 3 ( 2 + 3 ) ln π = - 29.84287823
Doc 17
0.0117, 0.0133
testing/NTCIR12_MathIR_WikiCorpus_v2.1.0/MathTagArticles/wpmath0000005/Articles/Stieltjes_constants.html