On the bivariate Mersenne Lucas polynomials and their properties

The main aim of this paper is to introduce new concept of bivariate Mersenne Lucas polynomials ${\left\{m_n(x,y)\right\}}_{n=0}^{\infty },$ we first give the recurrence relation of them. We then obtain Binet's formula, generating function, Catalan's identity and Cassini's identity for this type of polynomials. After that, we give the symmetric function, explicit formula and d'Ocagne's identity of bivariate Mersenne and bivariate Mersenne Lucas polynomials. By using the Binet's formula we obtain some well-known identities of these bivariate polynomials. Also, some summation formulas of bivariate Mersenne and bivariate Mersenne Lucas polynomials are investigated.