MATLAB: Recursion function-Chebyshev polynomials

chebyshev polynomialsrecursion

Question:
Chebyshev polynomials are defined recursively. Chebyshev polynomials are separated into two kinds: first and second. Chebyshev polynomials of the first kind, Tn(x), and of the second kind, Un(x), are defined by the following recurrence relations:
 Tn(x) = 1 if n = 0;
       = x if n = 1;
       =  2xTn−1(x) − Tn−2(x) otherwise;
Write a function with header [y] = myChebyshevPoly1(n,x), where y is the n-th Chebyshev polynomial of the first kind evaluated at x.Be sure your function can take array inputs for x. You may assume that x is a row vector. The output variable, y, must be a row vector also.
function [y] = myChebyshevPoly1(n,x)
% y = chebyshev polynimial
%Tn(x) = 1 if n=0
%Tn(x) =x if n=1
%Tn(x) = 2xTn-1(x) - Tn-2(x)
%function can take array 
% get array x
xleng=length(x);
    if n ==0
        y=1;
    elseif n==1
        y = x;
    else
        for i= 1: xleng
        y= 2*(x)*myChebyshevPoly1(n-1,x) - myChebyshevPoly1(n-2,x);
        end
    end
    end
      end
Comment: the code doesnt run because the array can't multiply together, how can I fix this?

Best Answer

Remember .* instead of *
But notice that in every iteration of your loop, you are overwriting all of y based on all of x. You need to rethink that loop.
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