@article{article_1607457, title={The Generalized Binomial Transform of the Bivariate Fibonacci and Lucas $p$-Polynomials}, journal={Mathematical Sciences and Applications E-Notes}, volume={13}, pages={65–71}, year={2025}, DOI={10.36753/mathenot.1607457}, author={Alp, Yasemin}, keywords={Binomial transform, Bivariate Fibonacci $p-$polynomials, Bivariate Lucas $p-$polynomials, Generating function}, abstract={The generalized binomial transforms of the bivariate Fibonacci $p-$polynomials and Lucas $p-$polynomials are introduced in this study. Furthermore, the generating functions of these polynomials are provided. Moreover, some relations are found for them. All results obtained are reduced to the $k-$binomial, falling binomial, rising binomial, and binomial transforms of the Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas, Fibonacci, and Lucas numbers.}, number={2}, publisher={Murat TOSUN}