Abel polynomials
The Abel polynomials in mathematics form a polynomial sequence, the nth term of which is of the form
The sequence is named after Niels Henrik Abel (1802-1829), the Norwegian mathematician.
This polynomial sequence is of binomial type: conversely, every polynomial sequence of binomial type may be obtained from the Abel sequence in the umbral calculus.
Examples[]
For a = 1, the polynomials are (sequence A137452 in the OEIS)
For a = 2, the polynomials are
References[]
- 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.
External links[]
Categories:
- Polynomials
- Algebra stubs