Peters polynomials

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

$\sum _{n=0}^{+\mathrm{\infty }}{s}_n(x)\frac{t^n}{n!}=\frac{(1+t{)}^x}{(1+(1+t{)}^{\lambda }{)}^{\mu }}$

(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, ISBN 978-0-387-03123-1, https://books.google.com/books?id=eihMuwkh4DsC 
• 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