Extended Generalized Fibonacci and Tribonacci Polynomials with some Properties
DOI:
https://doi.org/10.5644/SJM.21.01.05Keywords:
Extended Generalized Fibonacci Polynomials, Extended Generalized Tribonacci Polynomials, Binet's formula, generating function, Explicit sum formulaAbstract
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.
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