Returned 97 matches (100 formulae, 98 docs)
    Lookup 815.208 ms, Re-ranking 5857.326 ms
    Found 7348056 tuple postings, 3980090 formulae, 2222384 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
1.2495
testing/NTCIR/xhtml5/4/math0602613/math0602613_1_22.xhtml
(x+y)n=k=0n[nk]qykxn-k=k=0n[nk]q-1xkyn-k.
(ax+by)n=k=0n[nk]p,qan-kbkykxn-k=k=0n[nk]p-1,q-1bn-kakxkyn-k,

Doc 3
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 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
0.6189
-21.0000
12.0000
0.6189
testing/NTCIR/xhtml5/7/1007.3674/1007.3674_1_13.xhtml
En(r)(x)=l=0n(nl)El(r)xn-l=l=0n(nl)En-l(r)xl.

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
0.9342
testing/NTCIR/xhtml5/8/1202.2264/1202.2264_1_12.xhtml
(x+y)<qn=k=0n{nk}Q,qxn-kyk,
k=0n{nk}Q,qxn-kykx+k=0n{nk}Q,qqnxn-kyk+1

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
-11.0000
14.0000
0.4561
testing/NTCIR/xhtml5/10/q-alg9608008/q-alg9608008_1_15.xhtml
(x+y)n=k=0n[nk]qyn-kxk, n𝐙+.

Doc 16
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 17
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 18
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 19
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 20
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 21
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 22
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 23
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 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
0.7569
testing/NTCIR/xhtml5/1/math0211366/math0211366_1_12.xhtml
k=0n(nk)xkyn-kαk+k=0n(nk)xkyn-kβk
k=0n(nk)xkyn-kLk

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
-7.0000
10.0000
0.3964
testing/NTCIR/xhtml5/9/1309.2748/1309.2748_1_4.xhtml
Δ(xn)=i=0n(ni)xn-ixi

Doc 40
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 41
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 42
0.3964
-18.0000
8.0000
0.3964
testing/NTCIR/xhtml5/8/1202.2264/1202.2264_1_33.xhtml
(x+y)qn=k=0n[nk]qqk(k-1)2xn-kyk,

Doc 43
0.3964
-19.0000
8.0000
0.7611
testing/NTCIR/xhtml5/8/1202.2264/1202.2264_1_35.xhtml
(x+y)qn=k=0n[nk]q~qk(k-1)2xn-kyk,
(x+y)qn=k=0n(nk)qk(n-k+12)xn-kyk,

Doc 44
0.3964
-21.0000
8.0000
0.3964
testing/NTCIR/xhtml5/8/1202.2264/1202.2264_1_14.xhtml
(x+y)<qn=k=0n[nk]Q,qqk(k-1)2xn-kyk,

Doc 45
0.3964
-21.0000
8.0000
0.3964
testing/NTCIR/xhtml5/8/1202.2264/1202.2264_1_10.xhtml
(x+y)<qn=k=0n[nk]Q,qqk(k-1)2xn-kyk,

Doc 46
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 47
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 48
0.3788
-7.0000
9.0000
0.3788
testing/NTCIR/xhtml5/1/math0508233/math0508233_1_2.xhtml
En(x)=n=0n(nk)Ekxn-k,

Doc 49
0.3788
-7.0000
9.0000
0.3788
testing/NTCIR/xhtml5/9/1304.4509/1304.4509_1_25.xhtml
Bn(x)=k=0n(nk)Bkxn-k,

Doc 50
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 51
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 52
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 53
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 54
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 55
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 56
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 57
0.3646
-21.0000
7.0000
0.3646
testing/NTCIR/xhtml5/5/0805.2416/0805.2416_1_403.xhtml
i=0n-1(x+yqi)=k0[nk]qq(k2)xn-kyk.

Doc 58
0.3646
-21.0000
7.0000
0.3646
testing/NTCIR/xhtml5/5/0812.0779/0812.0779_1_156.xhtml
i=0n-1(x+yqi)=k0[nk]qq(k2)xn-kyk.

Doc 59
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 60
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 61
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 62
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 63
0.3596
-16.0000
10.0000
0.3596
testing/NTCIR/xhtml5/3/math0405544/math0405544_1_48.xhtml
(Δ(xn)u)(t)=k=0n(nk)(-x)n-ku(xkt).

Doc 64
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 65
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 66
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 67
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 68
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 69
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 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
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 72
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 73
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 74
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 75
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 76
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 77
0.3148
-9.0000
7.0000
0.3148
testing/NTCIR/xhtml5/9/1302.3104/1302.3104_1_5.xhtml
Bn(x)=k=0n(nk)Bn-kxk.

Doc 78
0.3148
-13.0000
10.0000
0.6296
testing/NTCIR/xhtml5/7/1008.4547/1008.4547_1_49.xhtml
=k=1n(n-1k-1)qxk(1-x)qn-k
=k=2n(n-2k-2)qxk(1-x)qn-k

Doc 79
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 80
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 81
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 82
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 83
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 84
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 85
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 86
0.2827
-43.0000
7.0000
0.2827
testing/NTCIR/xhtml5/1/0909.5512/0909.5512_1_7.xhtml
P~n(x)=k=0n(-1)n-k(nk)(n+kk)xk=k=0n(-1)n-k(n+kn-k)(2kk)xk.

Doc 87
0.2819
-22.0000
9.0000
0.2819
testing/NTCIR/xhtml5/1/1111.4880/1111.4880_1_66.xhtml
j=0n-k(-1)j(nj)Bkn-j(x)=(-1)n-k(nk)xn.

Doc 88
0.2505
-42.0000
6.0000
0.2505
testing/NTCIR/xhtml5/8/1109.4289/1109.4289_1_33.xhtml
S(n,0)=k=0n(n+1k)(-1)kS2(n-k,n-k)=k=0n(n+1k)(-1)k=(-1)n.

Doc 89
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 90
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 91
0.2293
-23.0000
7.0000
0.2293
testing/NTCIR/xhtml5/7/1005.4258/1005.4258_1_4.xhtml
k=0n(nk)x(x-kz)k-1(y+kz)n-k=(x+y)n,

Doc 92
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

Doc 93
0.2182
-21.0000
7.0000
0.2182
testing/NTCIR/xhtml5/8/1206.4004/1206.4004_1_4.xhtml
Qn-1(x)=k=0nw¯n,k(nk)xk(1-x)n-k

Doc 94
0.2182
-21.0000
5.0000
0.2182
testing/NTCIR/xhtml5/8/1208.3104/1208.3104_1_15.xhtml
(xD)n(x)=k=0n-1E(n,k)x2n-kyk+1.

Doc 95
0.2182
-44.0000
6.0000
0.2182
testing/NTCIR/xhtml5/3/math0411440/math0411440_1_115.xhtml
(x;n)=k=0n(-1)n-kq-(k2)(nk)q-1xk,xn=k=0nq(k2)(nk)q(x;k).

Doc 96
0.2050
-19.0000
6.0000
0.2050
testing/NTCIR/xhtml5/7/1005.1726/1005.1726_1_103.xhtml
=xyn+x2k=1n-1kyk-1(x+y)n-k-1

Doc 97
0.1734
-21.0000
5.0000
0.1734
testing/NTCIR/xhtml5/8/1208.3104/1208.3104_1_10.xhtml
Dn(x)=k=0n-1⟨⟨nk⟩⟩x2n-kyk+1.

Doc 98
0.1413
-24.0000
5.0000
0.1413
testing/NTCIR/xhtml5/9/math9207221/math9207221_1_4.xhtml
(x+y)nn!=k=0nxkk!yn-k(n-k)!