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.


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