Binomial transform of the bivariate Fibonacci quaternion polynomials and its properties

The primary aim of this work is to deal with binomial transforms of bivariate Fibonacci quaternion polynomial sequence. The binomial sequence of the bivariate Fibonacci quaternion polynomial is found, and then results are obtained for the recurrence relation, generating function and Binet formula. Furthermore, different types of sums are being sought for the polynomials. While working with bivariate Fibonacci quaternion polynomial sequence, we found the general formula for all sequences with quadratic recurrence relation, which includes the formulas in general terms for binomial transform. In the last part, matrix representations are derived for the corresponding binomial sequence.