Returned 94 matches (100 formulae, 99 docs)
    Lookup 22285.900 ms, Re-ranking 5553.149 ms
    Found 116531791 tuple postings, 11319459 formulae, 4586825 documents
[ formulas ] [ documents ] [ documents-by-formula ]

Doc 1
0.7459
-17.0000
14.0000
1.0788
testing/NTCIR/xhtml5/9/1306.6697/1306.6697_1_1.xhtml
Bn(k)(x)=l=0n(nl)Bn-l(k)xl=l=0n(nl)Bl(k)xn-l.
sn(x+y)=k=0n(nk)sk(y)xn-k=k=0n(nk)sn-k(y)xk,  (see[6,9]),

Doc 2
0.7293
-16.0000
21.0000
0.7293
testing/NTCIR/xhtml5/10/math9509223/math9509223_1_16.xhtml
(x+y)n=k=0n[nk]qykxn-k=k=0n[nk]q-1xkyn-k.

Doc 3
0.7293
-16.0000
21.0000
0.7293
testing/NTCIR/xhtml5/4/math0602613/math0602613_1_22.xhtml
(x+y)n=k=0n[nk]qykxn-k=k=0n[nk]q-1xkyn-k.

Doc 4
0.6338
-29.0000
18.0000
0.6338
testing/NTCIR/xhtml5/5/0811.4652/0811.4652_1_16.xhtml
fn(x,y2)=k0(n-k-1k)xn-2kyk+k0(n-k-2k)xn-2k-2yk+2.

Doc 5
0.5702
-12.0000
14.0000
0.5702
testing/NTCIR/xhtml5/8/1202.2507/1202.2507_1_35.xhtml
=i=0n(ni)μixn-i=i=0n(ni)xiμn-i.

Doc 6
0.5554
-3.0000
17.0000
0.5554
testing/NTCIR/xhtml5/8/1202.2264/1202.2264_1_1.xhtml
(x+y)n=k=0n(nk)xn-kyk,

Doc 7
0.5554
-4.0000
16.0000
0.5554
testing/NTCIR/xhtml5/8/1202.2264/1202.2264_1_34.xhtml
(x+y)n=k=0n[nk]Qxn-kyk.

Doc 8
0.5554
-8.0000
16.0000
0.5554
testing/NTCIR/xhtml5/8/1202.2264/1202.2264_1_12.xhtml
(x+y)<qn=k=0n{nk}Q,qxn-kyk,

Doc 9
0.5455
-23.0000
16.0000
0.5455
testing/NTCIR/xhtml5/7/1005.4218/1005.4218_1_22.xhtml
p(x):=k=0n(nk)1(k+d)!xk=k=0n(nk)1(n-k+d)!xn-k

Doc 10
0.5236
-3.0000
16.0000
0.5236
testing/NTCIR/xhtml5/6/0903.3216/0903.3216_1_21.xhtml
(x+y)n=k0(nk)xn-kyk,

Doc 11
0.5236
-6.0000
16.0000
0.8949
testing/NTCIR/xhtml5/6/0908.3248/0908.3248_1_58.xhtml
(x+y)n=k0(nk)𝒯1,1xn-kyk
(x-1)n=k0(nk)𝒯1,1(-1)n-kxkxn=k0(nk)𝒯1,1(x-1)k.

Doc 12
0.5065
-28.0000
16.0000
0.5065
testing/NTCIR/xhtml5/4/math0602672/math0602672_1_10.xhtml
zn=k=0n-1(n-1k)xkyn-k+k=0n-1(n-1k)xk+1yn-k-1.

Doc 13
0.4561
-10.0000
15.0000
0.4561
testing/NTCIR/xhtml5/10/q-alg9608008/q-alg9608008_1_14.xhtml
(x+y)n=k=0n(nk)yn-kxk, n𝐙+.

Doc 14
0.4561
-10.0000
15.0000
0.4561
testing/NTCIR/xhtml5/4/math0701369/math0701369_1_3.xhtml
(x+y)n=k=0n(nk)yn-kxk, n+,

Doc 15
0.4561
-13.0000
14.0000
0.4561
testing/NTCIR/xhtml5/4/math0511148/math0511148_1_88.xhtml
(x+y)n=k=0n[nk]qyn-kxk  (xy=qyx).

Doc 16
0.4427
-5.0000
14.0000
0.4427
testing/NTCIR/xhtml5/2/hep-th0207261/hep-th0207261_1_8.xhtml
(x+y)n=k=0nCnkxn-kyk

Doc 17
0.4427
-21.0000
12.0000
0.4427
testing/NTCIR/xhtml5/5/0810.0438/0810.0438_1_50.xhtml
nxn-1=k=1n(nk)Bn-k(x)=k=0n-1(nk)Bk(x),

Doc 18
0.4282
-5.0000
12.0000
0.4282
testing/NTCIR/xhtml5/1/math0009106/math0009106_1_56.xhtml
(x+y)n=0n(ni)qxiyn-i

Doc 19
0.4282
-5.0000
12.0000
0.4282
testing/NTCIR/xhtml5/7/1010.1981/1010.1981_1_38.xhtml
En(x)=k=0n(nk)xn-kEk

Doc 20
0.4282
-6.0000
13.0000
0.4282
testing/NTCIR/xhtml5/5/0708.1430/0708.1430_1_12.xhtml
(x+y)n=k=0n(nk)xkyn-k

Doc 21
0.4282
-6.0000
12.0000
0.4282
testing/NTCIR/xhtml5/1/math0502560/math0502560_1_9.xhtml
(x+y)n=j=0n(nj)xjyn-j

Doc 22
0.4282
-6.0000
9.0000
0.4282
testing/NTCIR/xhtml5/2/math0212344/math0212344_1_20.xhtml
(x+y)k=j=0k(kj)xjyk-j

Doc 23
0.4282
-6.0000
9.0000
0.4282
testing/NTCIR/xhtml5/9/math9301202/math9301202_1_19.xhtml
(a+b)n=k=0n(nk)akbn-k

Doc 24
0.4282
-7.0000
13.0000
0.4282
testing/NTCIR/xhtml5/5/0708.1430/0708.1430_1_37.xhtml
(x+y)n=k=0n(nk)qxkyn-k

Doc 25
0.4282
-7.0000
13.0000
0.4282
testing/NTCIR/xhtml5/10/math9803003/math9803003_1_51.xhtml
(x+y)n=k=0n(nk)qxkyn-k

Doc 26
0.4282
-7.0000
13.0000
0.4282
testing/NTCIR/xhtml5/5/0810.3554/0810.3554_1_121.xhtml
(x+y)n=k=0n(nk)xkyn-k.

Doc 27
0.4282
-7.0000
12.0000
0.4282
testing/NTCIR/xhtml5/3/math0408067/math0408067_1_81.xhtml
(x+y)n=j=0n(nj)xjyn-j,

Doc 28
0.4282
-8.0000
12.0000
0.4282
testing/NTCIR/xhtml5/8/1202.2264/1202.2264_1_5.xhtml
(x+y)n=k=0n[nk]qxkyn-k,

Doc 29
0.4282
-8.0000
11.0000
0.4282
testing/NTCIR/xhtml5/10/q-alg9704013/q-alg9704013_1_14.xhtml
             (x+y)n=r=0n[nr]xryn-r,             (A1)

Doc 30
0.4282
-8.0000
10.0000
0.4282
testing/NTCIR/xhtml5/2/math0204075/math0204075_1_8.xhtml
(x+z)n=i=0n(ni)qxizn-i.

Doc 31
0.4282
-10.0000
13.0000
0.8070
testing/NTCIR/xhtml5/2/quant-ph0105017/quant-ph0105017_1_111.xhtml
h(x)=(x+y)n=k=0n(nk)xkyn-k
xh(x)=nx(x+y)n-1=k=0n(nk)kxkyn-k

Doc 32
0.4282
-11.0000
13.0000
0.4282
testing/NTCIR/xhtml5/6/1002.1383/1002.1383_1_4.xhtml
(x+y)n=k=0n(nk)xkyn-k    (n)

Doc 33
0.4240
-18.0000
14.0000
1.4225
testing/NTCIR/xhtml5/1/math0211366/math0211366_1_12.xhtml
k=0n(nk)xkyn-kαk+k=0n(nk)xkyn-kβk
k=0n(nk)xkyn-kLk
k=0n(nk)xkyn-kFk=F2n,
k=0n(nk)xkyn-kLk=L2n.

Doc 34
0.4108
-6.0000
10.0000
0.4108
testing/NTCIR/xhtml5/8/1109.0326/1109.0326_1_4.xhtml
Bn(x)=k=0n(nk)Bkxn-k.

Doc 35
0.4108
-7.0000
11.0000
0.4108
testing/NTCIR/xhtml5/8/1202.0362/1202.0362_1_34.xhtml
fn(x)=k=0n(nk)xpkman-k

Doc 36
0.4108
-37.0000
10.0000
0.4108
testing/NTCIR/xhtml5/8/1202.0362/1202.0362_1_38.xhtml
fn(x)-x=k=ln(nk)xpkman-k=(k=ln(nk)xp(k-l)m(an-k)p-l)pl,

Doc 37
0.4039
-14.0000
14.0000
0.4039
testing/NTCIR/xhtml5/4/math0701369/math0701369_1_20.xhtml
(xqy)n=k=0n(nk)q(-1)n-kxkyn-k.

Doc 38
0.3964
-5.0000
12.0000
0.3964
testing/NTCIR/xhtml5/7/1105.3513/1105.3513_1_5.xhtml
(x+y)n=k(nk)xkyn-k.

Doc 39
0.3964
-8.0000
12.0000
0.3964
testing/NTCIR/xhtml5/7/1105.3513/1105.3513_1_11.xhtml
(x+y)n=k=0(nk)xkyn-k.

Doc 40
0.3964
-10.0000
12.0000
0.3964
testing/NTCIR/xhtml5/4/math0701369/math0701369_1_7.xhtml
(xqy)n=k=0n(nk)qxkyn-k.

Doc 41
0.3964
-21.0000
11.0000
0.3964
testing/NTCIR/xhtml5/6/0904.0407/0904.0407_1_55.xhtml
FnI(x,y,q)=2kn(n-kk)xn-2kykq(n2)-k.

Doc 42
0.3788
-6.0000
9.0000
0.3788
testing/NTCIR/xhtml5/9/1401.5618/1401.5618_1_16.xhtml
Bn(x)=k=0n(nk)Bkxn-k

Doc 43
0.3788
-6.0000
9.0000
0.3788
testing/NTCIR/xhtml5/5/0809.3277/0809.3277_1_62.xhtml
Bn(x)=k=0n(nk)Bkxn-k

Doc 44
0.3788
-13.0000
9.0000
0.3788
testing/NTCIR/xhtml5/7/1004.4989/1004.4989_1_20.xhtml
Bn(x)=k=0n(nk)Bkxn-k(x+ι)n.

Doc 45
0.3788
-31.0000
9.0000
0.3788
testing/NTCIR/xhtml5/3/math0407001/math0407001_1_16.xhtml
Bn(x+y)=k=0n(nk)Bk(x)yn-k,  Bn(x)=k=0n(nk)Bkxn-k,

Doc 46
0.3788
-31.0000
9.0000
0.3788
testing/NTCIR/xhtml5/3/math0304356/math0304356_1_38.xhtml
Bn(x+y)=k=0n(nk)Bk(x)yn-k,  Bn(x)=k=0n(nk)Bkxn-k,

Doc 47
0.3788
-35.0000
9.0000
0.3788
testing/NTCIR/xhtml5/5/0812.0962/0812.0962_1_3.xhtml
Bn(x)=k=0n(nk)Bkxn-kandEn(x)=k=0n(nk)Ek2k(x-12)n-k.

Doc 48
0.3714
-22.0000
11.0000
0.3714
testing/NTCIR/xhtml5/6/1001.2156/1001.2156_1_16.xhtml
km(m+rk)xkym-k=km(-rk)(-x)k(x+y)m-k,

Doc 49
0.3646
-4.0000
11.0000
0.3646
testing/NTCIR/xhtml5/6/0904.2672/0904.2672_1_21.xhtml
(x+1)n=k=0n(nk)xk

Doc 50
0.3646
-4.0000
10.0000
0.3646
testing/NTCIR/xhtml5/5/0810.0438/0810.0438_1_8.xhtml
=k=0n(nk)xn-kBk,

Doc 51
0.3646
-5.0000
11.0000
0.3646
testing/NTCIR/xhtml5/4/math0603405/math0603405_1_9.xhtml
(x+1)n=k=0n(nk)xk,

Doc 52
0.3646
-11.0000
11.0000
0.3646
testing/NTCIR/xhtml5/5/0707.1660/0707.1660_1_51.xhtml
pn,0(x,y)=k=0n(nk)xkyn-k

Doc 53
0.3646
-13.0000
11.0000
0.3646
testing/NTCIR/xhtml5/5/0707.1660/0707.1660_1_49.xhtml
pn,μ(x,y):=k=0n(nk)μxkyn-k.

Doc 54
0.3646
-20.0000
11.0000
0.3646
testing/NTCIR/xhtml5/8/1202.2264/1202.2264_1_35.xhtml
(x+y)qn=k=0n(nk)qk(n-k+12)xn-kyk,

Doc 55
0.3646
-25.0000
10.0000
0.3646
testing/NTCIR/xhtml5/8/1202.2264/1202.2264_1_39.xhtml
(x+y)q,Qn=k=0n[nk]q,Q(qQ)k(k-1)2xn-kyk.

Doc 56
0.3646
-38.0000
9.0000
0.6656
testing/NTCIR/xhtml5/9/1301.6979/1301.6979_1_85.xhtml
f=k=0n(nk)ξk(αx¯+βy¯)k(γx¯+δy¯)n-k=k=0n(nk)ξ¯kx¯ky¯n-k
f=k=0n(nk)ξkxkyn-k

Doc 57
0.3596
-8.0000
12.0000
0.3596
testing/NTCIR/xhtml5/10/q-alg9608008/q-alg9608008_1_17.xhtml
(x+y)n=k=0ncn,kyn-kxk

Doc 58
0.3596
-13.0000
12.0000
0.3596
testing/NTCIR/xhtml5/6/0907.5420/0907.5420_1_135.xhtml
Mn(x)=k=0n(nk)(n-1)n-k¯2kxk¯

Doc 59
0.3328
-10.0000
9.0000
0.3328
testing/NTCIR/xhtml5/3/math0402078/math0402078_1_13.xhtml
(x+ψa)n=k0(nk)ψakxn-k

Doc 60
0.3328
-10.0000
9.0000
0.3328
testing/NTCIR/xhtml5/3/math0402078/math0402078_1_12.xhtml
(x+ψa)n=k0(nk)ψakxn-k

Doc 61
0.3328
-12.0000
10.0000
0.3328
testing/NTCIR/xhtml5/7/1004.4173/1004.4173_1_40.xhtml
Hn(x+y)=k=0n(nk)Hn-k(x)yk

Doc 62
0.3328
-12.0000
10.0000
0.3328
testing/NTCIR/xhtml5/5/0810.3554/0810.3554_1_122.xhtml
(x+y)n=k=0n(nk)(x)k(y)n-k.

Doc 63
0.3328
-13.0000
10.0000
0.3328
testing/NTCIR/xhtml5/8/1207.2312/1207.2312_1_56.xhtml
Bn(x+y)=k=0n(nk)Bk(x)yn-k.

Doc 64
0.3328
-13.0000
10.0000
0.3328
testing/NTCIR/xhtml5/9/1302.3115/1302.3115_1_27.xhtml
Bn(x+y)=k=0n(nk)Bk(x)yn-k.

Doc 65
0.3328
-14.0000
10.0000
0.3328
testing/NTCIR/xhtml5/5/0810.3554/0810.3554_1_110.xhtml
pn(x+y)=k=0n(nk)pk(x)pn-k(y)

Doc 66
0.3328
-14.0000
10.0000
0.3328
testing/NTCIR/xhtml5/3/math0407181/math0407181_1_7.xhtml
pn(x+y)=k=0n(nk)pn-k(x)pk(y)

Doc 67
0.3328
-14.0000
10.0000
0.3328
testing/NTCIR/xhtml5/5/0810.3554/0810.3554_1_119.xhtml
pn(x+y)=k=0n(nk)pk(x)pn-k(y)

Doc 68
0.3328
-14.0000
10.0000
0.3328
testing/NTCIR/xhtml5/5/0810.3554/0810.3554_1_99.xhtml
sn(x+y)=k=0n(nk)sk(x)pn-k(y)

Doc 69
0.3328
-15.0000
10.0000
0.6657
testing/NTCIR/xhtml5/7/1105.4317/1105.4317_1_21.xhtml
pn(x+y)=k=0n(nk)pk(x)pn-k(y).
sn(x+y)=k=0n(nk)pk(x)sn-k(y),

Doc 70
0.3328
-15.0000
10.0000
0.3328
testing/NTCIR/xhtml5/5/math0703452/math0703452_1_21.xhtml
Bn(x+yi)=k=0n(nk)Bk(x)(yi)n-k

Doc 71
0.3328
-15.0000
10.0000
0.3328
testing/NTCIR/xhtml5/1/math0406378/math0406378_1_13.xhtml
fn(x+y)=k=0n(nk)fk(x)fn-k(y).

Doc 72
0.3328
-15.0000
10.0000
0.3328
testing/NTCIR/xhtml5/2/math0112194/math0112194_1_90.xhtml
Pn(x+y)=k=0n(nk)Pk(x)Pn-k(y).

Doc 73
0.3328
-15.0000
10.0000
0.3328
testing/NTCIR/xhtml5/2/math0112194/math0112194_1_88.xhtml
Pn(x+y)=k=0n(nk)Pk(x)Pn-k(y).

Doc 74
0.3328
-15.0000
7.0000
0.3328
testing/NTCIR/xhtml5/1/1111.4880/1111.4880_1_64.xhtml
j=0n-k(nj)xj-kBkn-j(x)=(nk).

Doc 75
0.3328
-16.0000
10.0000
0.3328
testing/NTCIR/xhtml5/7/1102.1493/1102.1493_1_36.xhtml
n(x+y;λ)=k=0n(nk)n-k(x;λ)yk

Doc 76
0.3328
-17.0000
10.0000
0.3328
testing/NTCIR/xhtml5/7/1011.3833/1011.3833_1_26.xhtml
Bn(m)(x+y)=k=0n(nk)Bk(m)(y)xn-k.

Doc 77
0.3328
-17.0000
10.0000
0.3328
testing/NTCIR/xhtml5/7/1101.0900/1101.0900_1_115.xhtml
k=mn(nk)xkyn-k(nm)xm(x+y)n-m.

Doc 78
0.3328
-37.0000
10.0000
0.3328
testing/NTCIR/xhtml5/5/0810.0438/0810.0438_1_9.xhtml
Bn(x+y)=k=0n(nk)Bk(x)yn-kandEn(x+y)=k=0n(nk)Ek(x)yn-k.

Doc 79
0.3273
-10.0000
10.0000
0.3273
testing/NTCIR/xhtml5/3/math0406323/math0406323_1_3.xhtml
𝐁n=k=0n(nk)(2y)n-kxk𝐀k.

Doc 80
0.3273
-25.0000
9.0000
0.3273
testing/NTCIR/xhtml5/7/1004.0578/1004.0578_1_55.xhtml
An=k=0n(nk)2(n+kk),  Bn=k=0n(nk)2(n+kk)2,

Doc 81
0.3273
-37.0000
10.0000
0.3273
testing/NTCIR/xhtml5/6/0908.3248/0908.3248_1_59.xhtml
Φn(x)=k0(nk)𝒯1,q(-1)n-kq(n-k2)xkxn=k0(nk)𝒯1,qΦk(x)

Doc 82
0.3273
-43.0000
10.0000
0.3273
testing/NTCIR/xhtml5/7/1008.4547/1008.4547_1_25.xhtml
Δqnf(0)=k=0n(nk)q(-1)kq(k2)f(n-k)=k=0n(nk)q(-1)n-kq(n-k2)f(k).

Doc 83
0.3148
-5.0000
10.0000
0.3148
testing/NTCIR/xhtml5/9/1301.3658/1301.3658_1_17.xhtml
(1+x)n=k=0n(nk)xk

Doc 84
0.3148
-6.0000
10.0000
0.3148
testing/NTCIR/xhtml5/6/0910.1263/0910.1263_1_46.xhtml
(1+x)n=k=0n(nk)xk,

Doc 85
0.3057
-22.0000
10.0000
0.6005
testing/NTCIR/xhtml5/8/1109.0141/1109.0141_1_12.xhtml
Kn(x)=i=1nqik=n-i+1n(nk)xk(1-x)n-k.
Hn(x)=i=1nqik=in(nk)xk(1-x)n-k

Doc 86
0.3057
-22.0000
10.0000
0.3057
testing/NTCIR/xhtml5/7/1005.4218/1005.4218_1_65.xhtml
A(x)=k=0n(nk)akxk,  B(x)=k=0n(nk)bkxk,

Doc 87
0.3010
-11.0000
7.0000
0.3010
testing/NTCIR/xhtml5/8/1109.4289/1109.4289_1_42.xhtml
k(nk)yn-kBk(x)=Bn(x+y).

Doc 88
0.3010
-15.0000
9.0000
0.3010
testing/NTCIR/xhtml5/4/math0507210/math0507210_1_63.xhtml
Tk(xn)=h=0n-k(n-h-1k-1)xh.

Doc 89
0.3010
-16.0000
9.0000
0.3010
testing/NTCIR/xhtml5/7/1012.0222/1012.0222_1_20.xhtml
Δ(xin)=k=0n(nk)qixikxin-k.

Doc 90
0.3010
-37.0000
6.0000
0.3010
testing/NTCIR/xhtml5/7/1011.3833/1011.3833_1_2.xhtml
q~n=k=0n(nk)2  p~n=k=0n(nk)2(n+k)!(Hn+k+2Hn-k-2Hk),

Doc 91
0.2948
-17.0000
10.0000
0.2948
testing/NTCIR/xhtml5/5/0710.5556/0710.5556_1_15.xhtml
(1+x)n=k=0n(nk)xk=k=0nCknxk,

Doc 92
0.2827
-21.0000
9.0000
0.2827
testing/NTCIR/xhtml5/7/1005.4218/1005.4218_1_78.xhtml
B(x)=k=0n(nk)(n+dk+d)(n-k+dn-k)xk

Doc 93
0.2827
-38.0000
9.0000
0.2827
testing/NTCIR/xhtml5/1/0911.1325/0911.1325_1_13.xhtml
-k=0n(nk)xkm=1n-k(-x)mm=k=1n(nk)xkm=1k1m+n-k.

Doc 94
0.2726
-14.0000
9.0000
0.2726
testing/NTCIR/xhtml5/9/1301.3669/1301.3669_1_2.xhtml
=nnξ(n)=k=0n(nk)kk(n-k)n-k,

Doc 95
0.2622
-14.0000
9.0000
0.2622
testing/NTCIR/xhtml5/9/1301.3669/1301.3669_1_1.xhtml
=k=0n(nk)(kn)k(n-kn)n-k,

Doc 96
0.2373
-12.0000
6.0000
0.2373
testing/NTCIR/xhtml5/10/math9412226/math9412226_1_20.xhtml
s(n)=k(nk)2=k=0n(nk)2

Doc 97
0.2373
-14.0000
6.0000
0.2373
testing/NTCIR/xhtml5/10/math9603215/math9603215_1_34.xhtml
s(n)=kZ(nk)2=k=0n(nk)2

Doc 98
0.2373
-31.0000
6.0000
0.2373
testing/NTCIR/xhtml5/7/1011.3833/1011.3833_1_4.xhtml
qn=k=0n(nk)2k!,  pn=k=0n(nk)2k!(2Hn-k-Hk).

Doc 99
0.2182
-15.0000
7.0000
0.2182
testing/NTCIR/xhtml5/3/math-ph0306032/math-ph0306032_1_46.xhtml
k=0n(nk)xk-k=p+1n(nk)xk