In mathematics, the Boole polynomials sn(x) are polynomials given by the generating function

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

(Roman 1984), (Jordan 1939).

## See also

* Umbral calculus
* Peters polynomials, a generalization of Boole polynomials.

## 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
* Boole, G. (1860/1970), Calculus of finite differences.
* Jordan, Charles (1939), Calculus of Finite Differences, Hungarian Agent Eggenberger Book-Shop, Budapest, Reprinted by Chelsea 1965, ISBN 978-0-8284-0033-6, https://books.google.com/books?id=3RfZOsDAyQsC
* 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