They are a generalized type of Brenke polynomial, and generalize the Appell polynomials.
The q-difference polynomials satisfy the relation where the derivative symbol on the left is the q-derivative.
, this becomes the definition of the Appell polynomials: The generalized generating function for these polynomials is of the type of generating function for Brenke polynomials, namely where
is the q-factorial and is the q-Pochhammer symbol.
gives a sequence of q-difference polynomials.