$q$-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.

DOI

10.3906/mat-1506-56

Keywords

Riordan representation, Pascal matrices, $q$-calculus

First Page

1038

Last Page

1048

Recommended Citation

TUĞLU, N, YEŞİL, F, DZIEMIANCZUK, M, & KOÇER, E. G (2016). $q$-Riordan array for $q$-Pascal matrix and its inverse matrix. Turkish Journal of Mathematics 40 (5): 1038-1048. https://doi.org/10.3906/mat-1506-56