Fibonacci Polynomial
The 
Polynomials obtained by setting 
and 
in the Lucas PolynomialSequence. (The corresponding 
Polynomials are called LucasPolynomials.) The Fibonacci polynomials are defined by the Recurrence Relation
 | (1) |
and 
. They are also given by the explicit sum formula | (2) |
is the Floor Function and 
is a Binomial Coefficient. The firstfew Fibonacci polynomials are |  |  | |
 | |  | |
 | |  | |
 | |  | |
 | |  |
The Fibonacci polynomials are normalized so that
 | (3) |
s are Fibonacci Numbers.The Fibonacci polynomials are related to the Morgan-Voyce Polynomials by
 | |  | (4) |
 | |  | (5) |
(Swamy 1968).See also Brahmagupta Polynomial, Fibonacci Number, Morgan-Voyce Polynomial
References
Swamy, M. N. S. ``Further Properties of Morgan-Voyce Polynomials.'' Fib. Quart. 6, 167-175, 1968.
- Dendrite Fractal
- Denjoy Integral
- Denominator
- Dense
- Density
- Density (Polygon)
- Density (Sequence)
- Denumerable Set
- Denumerably Infinite
- de Polignac's Conjecture
- Depth (Graph)
- Depth (Size)
- Depth (Statistics)
- Depth (Tree)
- Derangement
- de Rham Cohomology
- Derivative
- Derivative Test
- Derived Set
- Dervish
- Desargues' Theorem
- Descartes Circle Theorem
- Descartes-Euler Polyhedral Formula
- Descartes Folium
- Descartes' Formula