Abel polinomlari

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

$p_{n}(x)=x(x-an)^{n-1}.$

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

$p_{0}(x)=1;$

$p_{1}(x)=x;$

$p_{2}(x)=-2x+x^{2};$

$p_{3}(x)=9x-6x^{2}+x^{3};$

$p_{4}(x)=-64x+48x^{2}-12x^{3}+x^{4};$

a = 2 uchun polinomlar

$p_{0}(x)=1;$

$p_{1}(x)=x;$

$p_{2}(x)=-4x+x^{2};$

$p_{3}(x)=36x-12x^{2}+x^{3};$

$p_{4}(x)=-512x+192x^{2}-24x^{3}+x^{4};$

$p_{5}(x)=10000x-4000x^{2}+600x^{3}-40x^{4}+x^{5};$

$p_{6}(x)=-248832x+103680x^{2}-17280x^{3}+1440x^{4}-60x^{5}+x^{6};$

Manbalar

• Rota, Gian-Carlo; Shen, Jianhong; Taylor, Brian D. (1997). "All Polynomials of Binomial Type Are Represented by Abel Polynomials". Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. Series 4 25 (3–4): 731–738. http://www.numdam.org/item?id=ASNSP_1997_4_25_3-4_731_0. 

Havolalar

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