MATLAB: Series expansion: looping over different inputs

approximationserror functioninfinite seriesloopsseries

Say I have the approximation My question asks that I create two functions to calculate this approximation for an interval of x-values and a given N, using only 1 for loop for one function and 1 while loop for the other The first should loop over the values n = 0, . . . , N whilst the second should loop over the input x-values.
I dont understand the difference in what the question is asking for. Should the first loop be something like 
function [x,N]=T(x,N)
....
    for i=1:N
    ....
    end
    end
Whilst the second as something like 
function [x,N]=T(x,N)
....
    while x>'something'
    ....
    end
    end
or am I meant to seperate the x and N to something like 
    function x=T(x) N=T(N)
Any help would be really appreciated

Best Answer

I think it is asking 
T=zeros(1,length(x));
for n=0:N
    T=T+(-1)^n*(x.^(2*n+1))/factorial(n);
end
for one of the loops and
t=zeros(1,length(x));
count=1;
n=1:N;
while count<=length(x)
    t(count)=sum((-1).^n.*(x(count).^(2*n+1))./factorial(n));
    count=count+1;
end
for the other while loop. It tests your understanding of array math manipulations.
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