TY - JOUR AU - E. Özkan AU - M. Uysal PY - 2023/05/10 Y2 - 2024/03/28 TI - $d$-Gaussian Fibonacci, $d$-Gaussian Lucas polynomials and their matrix representations JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 75 IS - 4 SE - Research articles DO - 10.37863/umzh.v75i4.6988 UR - https://umj.imath.kiev.ua/index.php/umj/article/view/6988 AB - UDC 517.5We define $d$-Gaussian Fibonacci polynomials and $d$-Gaussian Lucas polynomials. We present the matrix representations of these polynomials. By using the Riordan method, we obtain the factorizations of the Pascal matrix including the polynomials. In addition, we define the infinite $d$-Gaussian Fibonacci polynomial matrix and the $d$-Gaussian Lucas polynomial matrix and give their inverses. ER -