- Turkish Journal of Mathematics
- Vol: 40 Issue: 5
- $q$-Riordan array for $q$-Pascal matrix and its inverse matrix
$q$-Riordan array for $q$-Pascal matrix and its inverse matrix
Authors : Naim Tuğlu, Fatma Yeşil, Maciej Dziemianczuk, E. Gökçen Koçer
Pages : 1038-1048
View : 8 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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