Extended Generalized Fibonacci and Tribonacci Polynomials with some Properties

Source abstract

In this paper, we introduced the extended generalized Fibonacci polynomial sequence \{$Y_{2,n}$\} and extended generalized Tribonacci polynomial \{$Y_{3,n}$\} with arbitrary initial values and established a recursive matrix and then presented some properties of these. Further, we investigated some well-known identities like Binet's formula, Catalan's identity, Cassini's identity, d'Ocagne's identity, generating function, explicit sum formula, sum of first $n$ terms for the extended generalized Fibonacci polynomial sequence and extended generalized Tribonacci polynomial sequence.