q -Binomial Convolution and Transformations of q -Appell Polynomials.

In this paper, binomial convolution in the frame of quantum calculus is studied for the set A q of q-Appell sequences. It has been shown that the set A q of q-Appell sequences forms an Abelian group under the operation of binomial convolution. Several properties for this Abelian group structure A q have been studied. A new definition of the q-Appell polynomials associated with a random variable is proposed. Scale transformation as well as transformation based on expectation with respect to a random variable is used to present the determinantal form of q-Appell sequences. [ABSTRACT FROM AUTHOR]