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.