Polinomios de Abel

Para a=1, los polinomios son (sucesión A137452 en OEIS)

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

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

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

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

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

Para a=2, los polinomios son

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

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

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

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

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

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

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

• 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 Sér. 4 25 (3–4): 731-738. MR 1655539. Zbl 1003.05011.

• Weisstein, Eric W. «Abel Polynomial». En Weisstein, Eric W, ed. MathWorld (en inglés). Wolfram Research.