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Abel polinomlari

Matematikadagi Abel koʻphadlari koʻp nomli ketma- ketlikni hosil qiladi, uning n -chi hadi quyidagi koʻrinishga ega.

pn(x)=x(x−an)n−1.{\displaystyle p_n(x)=x(x-an)^{n-1}.}

Bu ketma-ketlik norvegiyalik kuchli matematik Niels Henrik Abel (1802-1829) sharafiga nomlangan.

Bu koʻp nomli ketma-ketlik binomial tipga ega: aksincha, binomial turdagi har bir polinom ketma-ketligini umbral hisobdagi Abel ketma-ketligidan olish ham mumkin.

Misollar

a = 1 uchun polinomlar

p0(x)=1;{\displaystyle p_0(x)=1;}
p1(x)=x;{\displaystyle p_1(x)=x;}
p2(x)=−2x+x2;{\displaystyle p_2(x)=-2x+x^2;}
p3(x)=9x−6x2+x3;{\displaystyle p_3(x)=9x-6x^2+x^3;}
p4(x)=−64x+48x2−12x3+x4;{\displaystyle p_4(x)=-64x +48x^2-12x^3+x^4;}

a = 2 uchun polinomlar

p0(x)=1;{\displaystyle p_0(x)=1;}
p1(x)=x;{\displaystyle p_1(x)=x;}
p2(x)=−4x+x2;{\displaystyle p_2(x)=-4x+x^2;}
p3(x)=36x−12x2+x3;{\displaystyle p_3(x)=36x-12x^2+x^3;}
p4(x)=−512x+192x2−24x3+x4;{\displaystyle p_4(x)=-512x +192x^2-24x^3+x^4;}
p5(x)=10000x−4000x2+600x3−40x4+x5;{\displaystyle p_5(x)=10000x-4000x^2+600x^3-40x^4+x^5;}
p6(x)=−248832x+103680x2−17280x3+1440x4−60x5+x6;{\displaystyle p_6(x)=-248832x+103680x^2-17280x^3+1440x^4-60x^5+x^6;}

Manbalar

Havolalar

  • Weisstein, Eric W. „Abel Polynomial“. MathWorld.
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