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 ]

0.7459
-17.0000
14.0000
Bn(k)(x)=l=0n(nl)Bn-l(k)xl=l=0n(nl)Bl(k)xn-l.

0.7293
-16.0000
21.0000
(x+y)n=k=0n[nk]qykxn-k=k=0n[nk]q-1xkyn-k.

0.6338
-29.0000
18.0000
fn(x,y2)=k0(n-k-1k)xn-2kyk+k0(n-k-2k)xn-2k-2yk+2.

0.5702
-12.0000
14.0000
=i=0n(ni)μixn-i=i=0n(ni)xiμn-i.

0.5554
-3.0000
17.0000
(x+y)n=k=0n(nk)xn-kyk,

0.5554
-4.0000
16.0000
(x+y)n=k=0n[nk]Qxn-kyk.

0.5554
-8.0000
16.0000
(x+y)<qn=k=0n{nk}Q,qxn-kyk,

0.5455
-23.0000
16.0000
p(x):=k=0n(nk)1(k+d)!xk=k=0n(nk)1(n-k+d)!xn-k

0.5236
-3.0000
16.0000
(x+y)n=k0(nk)xn-kyk,

0.5236
-6.0000
16.0000
(x+y)n=k0(nk)𝒯1,1xn-kyk

0.5065
-28.0000
16.0000
zn=k=0n-1(n-1k)xkyn-k+k=0n-1(n-1k)xk+1yn-k-1.

0.4561
-10.0000
15.0000
(x+y)n=k=0n(nk)yn-kxk, n𝐙+.
(x+y)n=k=0n(nk)yn-kxk, n+,

0.4561
-13.0000
14.0000
(x+y)n=k=0n[nk]qyn-kxk  (xy=qyx).

0.4427
-5.0000
14.0000
(x+y)n=k=0nCnkxn-kyk

0.4427
-21.0000
12.0000
nxn-1=k=1n(nk)Bn-k(x)=k=0n-1(nk)Bk(x),

0.4282
-5.0000
12.0000
En(x)=k=0n(nk)xn-kEk

0.4282
-5.0000
12.0000
(x+y)n=0n(ni)qxiyn-i

0.4282
-6.0000
13.0000
(x+y)n=k=0n(nk)xkyn-k

0.4282
-6.0000
12.0000
(x+y)n=j=0n(nj)xjyn-j

0.4282
-6.0000
9.0000
(x+y)k=j=0k(kj)xjyk-j

0.4282
-6.0000
9.0000
(a+b)n=k=0n(nk)akbn-k

0.4282
-7.0000
13.0000
(x+y)n=k=0n(nk)qxkyn-k

0.4282
-7.0000
13.0000
(x+y)n=k=0n(nk)xkyn-k.

0.4282
-7.0000
12.0000
(x+y)n=j=0n(nj)xjyn-j,

0.4282
-8.0000
12.0000
(x+y)n=k=0n[nk]qxkyn-k,

0.4282
-8.0000
11.0000
             (x+y)n=r=0n[nr]xryn-r,             (A1)

0.4282
-8.0000
10.0000
(x+z)n=i=0n(ni)qxizn-i.

0.4282
-10.0000
13.0000
h(x)=(x+y)n=k=0n(nk)xkyn-k

0.4282
-11.0000
13.0000
(x+y)n=k=0n(nk)xkyn-k    (n)

0.4240
-18.0000
14.0000
k=0n(nk)xkyn-kαk+k=0n(nk)xkyn-kβk

0.4108
-6.0000
10.0000
Bn(x)=k=0n(nk)Bkxn-k.

0.4108
-7.0000
11.0000
fn(x)=k=0n(nk)xpkman-k

0.4108
-37.0000
10.0000
fn(x)-x=k=ln(nk)xpkman-k=(k=ln(nk)xp(k-l)m(an-k)p-l)pl,

0.4039
-14.0000
14.0000
(xqy)n=k=0n(nk)q(-1)n-kxkyn-k.

0.3964
-5.0000
12.0000
(x+y)n=k(nk)xkyn-k.

0.3964
-8.0000
12.0000
(x+y)n=k=0(nk)xkyn-k.

0.3964
-10.0000
12.0000
(xqy)n=k=0n(nk)qxkyn-k.

0.3964
-21.0000
11.0000
FnI(x,y,q)=2kn(n-kk)xn-2kykq(n2)-k.

0.3788
-6.0000
9.0000
Bn(x)=k=0n(nk)Bkxn-k

0.3788
-13.0000
9.0000
Bn(x)=k=0n(nk)Bkxn-k(x+ι)n.

0.3788
-18.0000
12.0000
xh(x)=nx(x+y)n-1=k=0n(nk)kxkyn-k

0.3788
-31.0000
9.0000
Bn(x+y)=k=0n(nk)Bk(x)yn-k,  Bn(x)=k=0n(nk)Bkxn-k,

0.3788
-35.0000
9.0000
Bn(x)=k=0n(nk)Bkxn-kandEn(x)=k=0n(nk)Ek2k(x-12)n-k.

0.3714
-22.0000
11.0000
km(m+rk)xkym-k=km(-rk)(-x)k(x+y)m-k,

0.3714
-32.0000
13.0000
(x-1)n=k0(nk)𝒯1,1(-1)n-kxkxn=k0(nk)𝒯1,1(x-1)k.

0.3646
-4.0000
11.0000
(x+1)n=k=0n(nk)xk

0.3646
-4.0000
10.0000
=k=0n(nk)xn-kBk,

0.3646
-5.0000
11.0000
(x+1)n=k=0n(nk)xk,

0.3646
-11.0000
11.0000
pn,0(x,y)=k=0n(nk)xkyn-k

0.3646
-13.0000
11.0000
pn,μ(x,y):=k=0n(nk)μxkyn-k.

0.3646
-20.0000
11.0000
(x+y)qn=k=0n(nk)qk(n-k+12)xn-kyk,

0.3646
-25.0000
10.0000
(x+y)q,Qn=k=0n[nk]q,Q(qQ)k(k-1)2xn-kyk.

0.3646
-38.0000
9.0000
f=k=0n(nk)ξk(αx¯+βy¯)k(γx¯+δy¯)n-k=k=0n(nk)ξ¯kx¯ky¯n-k

0.3596
-8.0000
12.0000
(x+y)n=k=0ncn,kyn-kxk

0.3596
-13.0000
12.0000
Mn(x)=k=0n(nk)(n-1)n-k¯2kxk¯

0.3328
-5.0000
10.0000
k=0n(nk)xkyn-kLk

0.3328
-10.0000
10.0000
k=0n(nk)xkyn-kFk=F2n,
k=0n(nk)xkyn-kLk=L2n.

0.3328
-10.0000
9.0000
(x+ψa)n=k0(nk)ψakxn-k

0.3328
-12.0000
10.0000
(x+y)n=k=0n(nk)(x)k(y)n-k.

0.3328
-12.0000
10.0000
Hn(x+y)=k=0n(nk)Hn-k(x)yk

0.3328
-13.0000
10.0000
Bn(x+y)=k=0n(nk)Bk(x)yn-k.

0.3328
-14.0000
10.0000
pn(x+y)=k=0n(nk)pn-k(x)pk(y)

0.3328
-14.0000
10.0000
pn(x+y)=k=0n(nk)pk(x)pn-k(y)
sn(x+y)=k=0n(nk)sk(x)pn-k(y)

0.3328
-15.0000
10.0000
pn(x+y)=k=0n(nk)pk(x)pn-k(y).
fn(x+y)=k=0n(nk)fk(x)fn-k(y).
Pn(x+y)=k=0n(nk)Pk(x)Pn-k(y).
sn(x+y)=k=0n(nk)pk(x)sn-k(y),

0.3328
-15.0000
10.0000
Bn(x+yi)=k=0n(nk)Bk(x)(yi)n-k

0.3328
-15.0000
7.0000
j=0n-k(nj)xj-kBkn-j(x)=(nk).

0.3328
-16.0000
10.0000
n(x+y;λ)=k=0n(nk)n-k(x;λ)yk

0.3328
-17.0000
10.0000
k=mn(nk)xkyn-k(nm)xm(x+y)n-m.

0.3328
-17.0000
10.0000
Bn(m)(x+y)=k=0n(nk)Bk(m)(y)xn-k.

0.3328
-37.0000
10.0000
Bn(x+y)=k=0n(nk)Bk(x)yn-kandEn(x+y)=k=0n(nk)Ek(x)yn-k.

0.3328
-37.0000
10.0000
sn(x+y)=k=0n(nk)sk(y)xn-k=k=0n(nk)sn-k(y)xk,  (see[6,9]),

0.3273
-10.0000
10.0000
𝐁n=k=0n(nk)(2y)n-kxk𝐀k.

0.3273
-25.0000
9.0000
An=k=0n(nk)2(n+kk),  Bn=k=0n(nk)2(n+kk)2,

0.3273
-37.0000
10.0000
Φn(x)=k0(nk)𝒯1,q(-1)n-kq(n-k2)xkxn=k0(nk)𝒯1,qΦk(x)

0.3273
-43.0000
10.0000
Δqnf(0)=k=0n(nk)q(-1)kq(k2)f(n-k)=k=0n(nk)q(-1)n-kq(n-k2)f(k).

0.3148
-5.0000
10.0000
(1+x)n=k=0n(nk)xk

0.3148
-6.0000
10.0000
(1+x)n=k=0n(nk)xk,

0.3057
-22.0000
10.0000
Kn(x)=i=1nqik=n-i+1n(nk)xk(1-x)n-k.

0.3057
-22.0000
10.0000
A(x)=k=0n(nk)akxk,  B(x)=k=0n(nk)bkxk,

0.3010
-8.0000
7.0000
f=k=0n(nk)ξkxkyn-k

0.3010
-11.0000
7.0000
k(nk)yn-kBk(x)=Bn(x+y).

0.3010
-15.0000
9.0000
Tk(xn)=h=0n-k(n-h-1k-1)xh.

0.3010
-16.0000
9.0000
Δ(xin)=k=0n(nk)qixikxin-k.

0.3010
-37.0000
6.0000
q~n=k=0n(nk)2  p~n=k=0n(nk)2(n+k)!(Hn+k+2Hn-k-2Hk),

0.2948
-17.0000
10.0000
(1+x)n=k=0n(nk)xk=k=0nCknxk,

0.2948
-18.0000
9.0000
Hn(x)=i=1nqik=in(nk)xk(1-x)n-k

0.2827
-21.0000
9.0000
B(x)=k=0n(nk)(n+dk+d)(n-k+dn-k)xk

0.2827
-38.0000
9.0000
-k=0n(nk)xkm=1n-k(-x)mm=k=1n(nk)xkm=1k1m+n-k.

0.2726
-14.0000
9.0000
=nnξ(n)=k=0n(nk)kk(n-k)n-k,

0.2622
-14.0000
9.0000
=k=0n(nk)(kn)k(n-kn)n-k,

0.2373
-12.0000
6.0000
s(n)=k(nk)2=k=0n(nk)2

0.2373
-14.0000
6.0000
s(n)=kZ(nk)2=k=0n(nk)2

0.2373
-31.0000
6.0000
qn=k=0n(nk)2k!,  pn=k=0n(nk)2k!(2Hn-k-Hk).

0.2182
-15.0000
7.0000
k=0n(nk)xk-k=p+1n(nk)xk