Fibonacci Polynomial Identities

Math 242 Modern Computational Mathematics

Preliminary Code

Here is our Fibonacci list module from previous class sessions. This returns a list of Fibonacci numbers (Subscript[F, 0]),(Subscript[F, 1]),...,(Subscript[F, n]).

fibonacciList[n_]:=Module[{fibList=Table[0,n+1]},
(* set the initial values (Subscript[F, 0]) and (Subscript[F, 1]) *)
fibList[[2]]=1;

(* compute (Subscript[F, 2]) through (Subscript[F, n]) and store them in the list *)
Do[
fibList[[i]]=fibList[[i-1]]+fibList[[i-2]]
,{i,3,n+1}];

(* return the list *)
fibList
]

First we create a big list of Fibonacci numbers.

fibList=fibonacciList[1000];

Next we create a little function f to adjust the indexing to match the usual mathematical notation. (That is, (Subscript[F, 0])=0, (Subscript[F, 1])=1, etc.)

f[n_]:=fibList[[n+1]]

Today we will discover another Fibonacci identity