q-ALMOST RIORDAN ARRAYS

Abstract

Our focus is on examining a group of Riordan arrays, in which each member is represented by a triple of power series that called almost Riordan array. If we take a triple of power series is chosen as a $q$-functions,  we identify the $q$-analogue of the almost-Riordan arrays and called $q$-almost Riordan arrays. In addition, we obtain the fundamental theorem for  $q$-almost Riordan arrays (FT$q$ARA). Also, we show that suitably chosen a pair of  $q$-almost Riordan arrays can lead to  new formulas for multiplication  of any $q$-almost Riordan arrays. Finally, by the help of the FT$q$ARA, the generating function is derived for some  row sums  of $q$-almost Riordan matrices.