Recurrence. Consider the following $3-$term recurrence:

$T_0(x)=1,$

$T_1(x)=x$

$T_n(x)=2x{T}_{n-1}(x)-T_{n-2}(x)$ for $n>1$

This recurrence is valid for any $x,$ but defines a special set of polynomials when xin$[-1,1].$

Create a Matlab $($or python$)$ function that computes Tn$($x$)$ iteratively with the recurrence, taking n and x as inputs. $($Hint: modify f i b o n a c c i $\_$ d i r e c t $2.$ m$)$

fibonacci$\_$recursive$2.$m Generate Fibonacci number using faster recursion

function $F=$ fibonacci$\_$recursive$2($n$)$

if $n==0$

$F=0$;

elseif $n==1$

$F=1$;

elseif $n==2$

$F=1$;

else

if mod$(n,2)$

$F=$ fibonacci$\_$recursive $2(\frac{n-1}{2}{)}^{{?}^{{?}^{?}}}2+$ fibonacci$\_$recursive $2(\frac{n+1}{2}{)}^{{?}^{{?}^{?}}}2$;

else

$F=$ fibonacci$\_$recursive $2(\frac{n}{2}+1{)}^{{?}^{{?}^{?}}}2-fibonacc{i}_r$ecursive$2(\frac{n}{2}-1{)}^{{?}^{{?}^{?}}}2$;

end

end