On Properties of Generalized Bi-Variate Bi-Periodic Fibonacci Polynomials

Abstract

We define a generalized Bi-variate Bi-periodic Fibonacci like polynomials with initial conditions V_0 (x,y)=a_0,V_1 (x,y)=a_1 and for n≥2 with the recurrence relation V_n (x,y)=p〖xV〗_(n-1) (x,y)+qyV_(n-2) (x,y)if n is even and V_n (x,y)=r〖xV〗_(n-1) (x,y)+syV_(n-2) (x) if n is odd.If we set a_0=0 and a_1=1 then the GeneralizedBi-variate Bi-periodic Fibonacci polynomial B_n (x,y) will be obtained andWe will derive various identities like Catalan’s identity, d’Ocagne’s identity,Cassini’s identity and Gelin Cesaroidentity along with Generating function and Binet’s formula for the Bi-variate Bi-periodic Fibonacci polynomial.