How can I write an algorithm in maple that gives me a lisft of the Fibonacci polynomies between two numbers using the recursion:
F1(x) = 1
F2(x) = x
Fn+1(x) = x*Fn(x) + Fn−1(x)
if anyone knows please help me!!
Yes, it's the rsolve command.
i.e., to generate the closed-form for the nth Fibonacci number type:
rsolve({f(n)=f(n-1)+f(n-2),f(0)=1,f(1)=1},{f(n)});
This will give you:
Which is the formula we get from Binet's formula.
By tweaking it accordingly, you should get the polynomials:
The closed-form is