// Workers AI · dad joke modeWhy did Boole polynomials go to therapy? Because they had true false hopes.

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

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

See also

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

Further reading

• 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, ISBN 978-0-387-03123-1, MR 0094466 {{citation}}: ISBN / Date incompatibility (help)
• Boole, G. (1860/1970), Calculus of finite differences.