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- Title
IDENTITIES FOR THE GENERALIZED FIBONACCI POLYNOMIAL.
- Authors
Flórez, Rigoberto; McAnally, Nathan; Mukherjee, Antara
- Abstract
A second order polynomial sequence is of Fibonacci type (Lucas type) if its Binet formula is similar in structure to the Binet formula for the Fibonacci (Lucas) numbers. In this paper we generalize identities from Fibonacci numbers and Lucas numbers to Fibonacci type and Lucas type polynomials. A Fibonacci type polynomial is equivalent to a Lucas type polynomial if they both satisfy the same recurrence relations. Most of the identities provide relationships between two equivalent polynomials. In particular, each type of identities in this paper relate the following polynomial sequences: Fibonacci with Lucas, Pell with Pell-Lucas, Fermat with Fermat-Lucas, both types of Chebyshev polynomials, Jacobsthal with Jacobsthal-Lucas and both types of Morgan-Voyce.
- Subjects
FIBONACCI sequence; LUCAS numbers; POLYNOMIALS; RECURRENT equations; IDENTITIES (Mathematics)
- Publication
Integers: Electronic Journal of Combinatorial Number Theory, 2018, Vol 18B, p1
- ISSN
1553-1732
- Publication type
Article