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:1002-8743(2006)01-0098-08n1,2(11,530001;21,530003):n,:,,,.:n;;;;:O151122:A,,..1:()(),n,.1nx1-a1x2x3xnx1x2-a2x3xnx1x2x3-a3xnx1x2x3xn-an.x1-a1x2x3xnx1x2-a2x3xnx1x2x3-a3xnx1x2x3xn-an=x1-a1x2x3xna1-a200a10-a30a100-an=a1a2anx1a1-1x2a2x3a3xnan1-10010-10100-1=a1a2anni=1xiai-1x2a2x3a3xnan0-10000-10000-1=(-1)n-1a1a2anni=1xiai-1.:2006-03-06:(2005B015):(1974-),,,,,.20063()Mar.2006231JournalofGuangxiTeachersEducationUniversity(NaturalScienceEdition)Vol.23No.12na1xxxxa2xxxxa3xxxxan.a1xxxxa2xxxxa3xxxxan=a1-x000x0a2-x00x00a3-x0x000an-1-xxx-anx-anx-anx-anan=(a1-x)(a2-x)(an-x)1000x/(a1-x)0100x/(a2-x)0010x/(a3-x)0001x/(an-1-x)0000an/(an-x)+n-1i=1x/(ai-x)=(a1-x)(a2-x)(an-x)(x/(a1-x)+x/(a2-x)++x/(an-1-x)+an/(an-x)).().()(),,.:1+a111111+a211111+a311111+ana01111a10010a20100an123n-103n-1-20n-1-2-30xaaaaxaaaaxaaaax.2(),n()n+1,()(),().,:(1)(2)(3)(4)..1,:n99(1)31+a11+a211+an11+a21+a221+an21+an1+a2n1+ann.1+a11+a211+an11+a21+a221+an21+an1+a2n1+ann=100011+a11+a211+an111+a21+a221+an211+an1+a2n1+ann=1-1-1-11a1a21an11a2a22an21anan2ann=2-10-10-10-11a1a21an11a2a22an21ana2nann=20001a1a21an11a2a22an21ana2nann+-1-1-1-11a1a21an11a2a22an21ana2nann=20001a1a21an11a2a22an21ana2nann+-10001a1-1a21-a1an1-an-111a2-1a22-a2an2-an-121an-1a2n-anann-an-1n=20001a1a21an11a2a22an21ana2nann+-10001a1-1a1(a1-1)an-11(a1-1)1a2-1a2(a2-1)an-12(a2-1)1an-1an(an-1)an-1n(an-1)=2a1a21an1a2a22an2ana2nann-(a1-1)(a2-1)(an-1)1a1an-111a2an-121anan-1n=2a1a2an1a1an-111a2an-121anan-1n-(a1-1)(a2-1)(an-1)1a1an-111a2an-121anan-1n=[2a1a2an-(a1-1)(a2-1)(an-1)]1ijn(aj-ai).4nx1a2a3an-1ana1x2a3an-1ana1a2x3an-1ana1a2a3xn-1ana1a2a3an-1xn.100()23x1a2a3an-1ana1x2a3an-1ana1a2x3an-1ana1a2a3xn-1ana1a2a3an-1xn=x1a2a3an-1an1a1x2a3an-1an1a1a2x3an-1an1a1a2a3xn-1an1a1a2a3an-1xn1000001=x1-a1000010x2-a2000100x3-a3001000xn-1-an-1010000xn-an1-a1-a2-a3-an-1-an1=(x1-a1)(xn-an)100001010001001001000101000011-a1x1-a1-a2x2-a2-a3x3-a3-an-1xn-1-an-1-anxn-an1=(x1-a1)(xn-an)100001010000001000000100000010-a1x1-a1-a2x2-a2-a3x3-a3-an-1xn-1-an-1-anxn-an1+ni=1aixi-ai=(x1-a1)(x2-a2)(xn-an)1+a1x1-a1+a2x2-a2++anxn-an.(2)5n1x1x21xs-11xs+11xn11x2x22xs-12xs+12xn21xnx2nxs-1nxs+1nxnn.:1x1x21xs-11xs1xs+11xn11x2x22xs-12xs2xs+12xn21xnx2nxs-1nxsnxs+1nxnn1zz2zs-1zszs+1znn+1z,1,:n101zs(-1)n+1+s+1.:(1)(),()(),;(2)().:1+a11111+b11111+c11111+d111x1x2xnx21x22x2nxn-21xn-22xn-2nxn1xn2xnn1+a111111+a211111+a311111+an.3,.(),,,.6D=xa1a2an-1ana1xa2an-1ana1a2a3anx.D=x+ni=1aia1a2an-1anx+ni=1aixa2an-1anx+ni=1aia2a3anx=(x+ni=1ai)1a1a2an-1an1xa2an-1an1a2a3anx,xf(x),f(a1)=0,f(a2)=0,,f(an)=0,x=a1,a2,,an,,.:x-a1,x-a2,,x-an,D=k(x+a1+a2++an)(x-a1)(x-a2)(x-an),1,D=(x+a1+a2++an)(x-a1)(x-a2)(x-an).:,,.:111x1x2xnx21x22x2nxn-21xn-22xn-2nxn-11xn-12xn-1n0xyzx0zyyz0xzyx01+x11111-x11111+y11111-y.102()234(),.Dn,Dn-1,Dn,Dn-1,Dn-2,Dn,Dn-1,;Dn,Dn-1,Dn-2,Dn+aDn-1=b(Dn-1+aDn-2),,a,b,.(1)Dn,Dn-17Dn+1=xa1a2ana1xa2ana1a2a3ana1a2a3x.Dn+1=xa1a2an-10a1xa2an-10a1a2xan-10a1a2a3x0a1a2a3anx-an+xa1a2an-1ana1xa2an-1ana1a2xan-1ana1a2a3xana1a2a3anan=(x-an)Dn+(x-a1)(x-a2)(x-an)an,D1=x,D2(x+a1)(x-a1),D3=(x-a2)[(x+a1)(x-a1)]+a2(x-a1)(x-a2)=(x+a1+a2)(x-a1)(x-a2).Dn=(x+a1+a2++an-1)(x-a1)(x-a2)(x-an-1),Dn+1=(x-an)(x+a1+a2++an-1)(x-a1)(x-a2)(x-an-1)+an(x-a1)(x-a2)(x-an-1)(x-an)=(x+a1+a2+an-1+an)(x-a1)(x-a2)(x-an-1)(x-an).8Dn=x1yyyyzx2yyyzzx3yyzzzxn-1yzzzzxn.Dn=x1yyyyzx2yyyzzx3yyzzzxn-1yzzzzxn=x1yyyy+0zx2yyy+0zzx3yy+0zzzxn-1y+0zzzzy+xn-y=1,:n103x1yyyyzx2yyyzzx3yyzzzxn-1yzzzzy+x1yyy0zx2yy0zzx3y0zzzxn-10zzzzxn-y=x1-zy-zy-zy-z00x2-zy-zy-z000x3-zy-z0000xn-1-z0zzzzy+(xn-y)Dn-1=yn-1i=1(xi-z)+(xn-y)Dn-1.Dn=Dn=zn-1i=1(xi-y)+(xn-z)Dn-1=zn-1i=1(xi-y)+(xn-z)Dn-1.yz,:Dn=1z-yzni=1(xi-y)-yni=1(xi-z).y=z,:Dn=x1ni=2(xi-y)+yni=2nji(xj-y).(2)Dn,Dn-1,Dn-29Dn=a+bab0001a+bab0001a+b000001a+b.Dn=a+bab0001a+bab0001a+b000001a+b=(a+b)a+bab001a+b00001a+bn-1-ab1ab000a+b00001a+b=(a+b)a+bab001a+b00001a+bn-1-aba+bab001a+b00001a+bn-2=(a+b)Dn-1-abDn-2,Dn-aDn-1=b(Dn-1-aDn-2),Dn-aDn-1=b(Dn-1-aDn-2)=b2(Dn-2-aDn-3)==bn-2(D2-aD1),D2-aD1=b2,Dn-aDn-1=bn.(1)Dn-bDn-1=an.(2)104()23ab,(1)(2)Dn-1,Dn=an+1-bn+1a-b.a=b,Dn=aDn-1+an=a(aDn-2+an-1)+an=a2Dn-2+2an==an-1D1+(n-1)an=(n+1)an.10Dn=ab000cab000ca00000ca.9Dn=aDn-1-bcDn-2,Dn-x1Dn-1=x2(Dn-1-x1Dn-2),x1+x2=ax1x2=b,x1,x2x2-ax+b=0.10,75000275000270000075000272-1000-12-1000-12000002-1000-12.:(),.:cos100012cos100012cos0000012cos,+000+000+00000+000+.,(),(),,.,,,.,,.,,,.,.:[1].()[M].:,2003.[:]1,:n105