$q$-Riordan array for $q$-Pascal matrix and its inverse matrix

Authors: NAİM TUĞLU, FATMA YEŞİL, MACIEJ DZIEMIANCZUK, E. GÖKÇEN KOÇER

Abstract: In this paper, we prove the $q$-analogue of the fundamental theorem of Riordan arrays. In particular, by defining two new binary operations $\ast_{q} $ and $\ast _{1/q}$, we obtain a $q$-analogue of the Riordan representation of the $q$-Pascal matrix. In addition, by aid of the $q$-Lagrange expansion formula we get $q$-Riordan representation for its inverse matrix.

Keywords: Riordan representation, Pascal matrices, $q$-calculus

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