Peters polynomials

In mathematics, the Peters polynomials s_n(x) are polynomials studied by Peters (1956, 1956b) given by the generating function

[math]\displaystyle{ \displaystyle \sum_{n=0}^{+\infty} s_n(x)\frac{t^n}{n!} = \frac{(1+t)^x}{(1+(1+t)^\lambda)^{\mu}} }[/math]

(Roman 1984), (Boas Buck). They are a generalization of the Boole polynomials.

See also

• Umbral calculus

References

• Boas, Ralph P.; Buck, R. Creighton (1958), Polynomial expansions of analytic functions, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge., 19, Berlin, New York: Springer-Verlag, https://books.google.com/books?id=eihMuwkh4DsC 
• Peters, George Owen (1956), Schafer, Richard D., ed., "Boole polynomials of higher and negative orders", Bulletin of the A.M.S. 62 (1): 7, doi:10.1090/S0002-9904-1956-09972-0 
• Peters, George Owen (1956b), Schafer, Richard D., ed., "Boole polynomials and numbers of the second kind", Bulletin of the A.M.S. 62: 387, doi:10.1090/S0002-9904-1956-10046-3 
• Roman, Steven (1984), The umbral calculus, Pure and Applied Mathematics, 111, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers], ISBN 978-0-12-594380-2, https://books.google.com/books?id=JpHjkhFLfpgC  Reprinted by Dover, 2005