@article{Özkan_Uysal_2023, title={$d$-Gaussian Fibonacci, $d$-Gaussian Lucas polynomials and their matrix representations}, volume={75}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/6988}, DOI={10.37863/umzh.v75i4.6988}, abstractNote={<div class="page" title="Page 1"> <div class="layoutArea"> <div class="column"> <p>UDC 517.5</p> </div> </div> </div> <p>We define $d$-Gaussian Fibonacci polynomials and $d$-Gaussian Lucas polynomials.<span class="Apple-converted-space">&nbsp;</span>We present the matrix representations of these polynomials.<span class="Apple-converted-space">&nbsp;</span>By using the Riordan method, we obtain the factorizations of the<span class="Apple-converted-space">&nbsp;</span>Pascal matrix including the polynomials.<span class="Apple-converted-space">&nbsp;</span>In addition, we define the infinite $d$-Gaussian Fibonacci polynomial matrix and the $d$-Gaussian Lucas polynomial matrix and give their inverses.</p&gt;}, number={4}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Özkan, E. and Uysal, M.}, year={2023}, month={May}, pages={491 - 510} }