Boole polynomials

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

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

(Roman 1984, 4.5), (Jordan 1939, sections 113–117).

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., vol. 19, Berlin, New York: Springer-Verlag, MR 0094466
• Boole, G. (1860/1970), Calculus of finite differences.
• Jordan, Charles (1939), Calculus of Finite Differences, Hungarian Agent Eggenberger Book-Shop, Budapest, ISBN 978-0-8284-0033-6, MR 0000441, Reprinted by Chelsea 1965
• Roman, Steven (1984), The umbral calculus, Pure and Applied Mathematics, vol. 111, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers], ISBN 978-0-12-594380-2, MR 0741185 Reprinted by Dover, 2005