Boole Polynomial

Polynomials  which form a Sheffer sequence with

			(1)
			(2)

and have generating function

(3)

The first few are

			(4)
			(5)
			(6)

Jordan (1965) considers the related polynomials  which form a Sheffer sequence with

			(7)
			(8)

These polynomials have generating function

(9)

The first few are

			(10)
			(11)
			(12)
			(13)

The Peters polynomials are a generalization of the Boole polynomials.

REFERENCES:

Boas, R. P. and Buck, R. C. Polynomial Expansions of Analytic Functions, 2nd print., corr. New York: Academic Press, p. 37, 1964.

Jordan, C. Calculus of Finite Differences, 3rd ed. New York: Chelsea, 1965.

Roman, S. The Umbral Calculus. New York: Academic Press, 1984.