Boole polynomials

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

$\sum s_n(x)t^n/n!=\frac{(1+t{)}^x}{1+(1+t{)}^{\lambda }}$

(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