Need help creating a "for loop" for the following series.

the above equation is used to determined certain polynomial coefficients. I tried creating a "for" loop for the function where y = 1,2,....,v and L0 = 1. where v is a scalar input like 3. I tried creating a "for loop" where instead starting from i = 0, it starts from 1, but the L vector (input) does not want sum up the correct values. I am suppose to get f2y = [0 -0.75 0 0.1875 0 -0.156] but cannot seem to work backwards. Please help!!!

Here is what I came up so far,

L = [1.5 0.75 0.125 0 0 0];
v = 3;
f2y = zeros(1,2*v);
 for y = 2:v,
   f2y(2) = 2*L(1)*L(3) + (-1)^(1) * L(2)^(2);
   for ii = 1:v,
     f2y(2*y) = (-1)^(ii-1)*2*L(ii)*L(2*y-ii) + (-1)^(y) * L(y+1)^(2);
   end
 end

[Star Strider]

‘where u is a scalar input like 3’

Unfortunately, u is nowhere to be found in the expression you posted. Could that be the problem?

[Wilmer]

meant "v" not "u".....

Answer 1

[Nalini Vishnoi]

In my understanding you are trying to convert the above equation to MATLAB code using 'for' loops.

The last term in the equation is outside the summation.

Since the L vector starts from 0, I would recommend appending the first index of vector L with a 1 and using L(t+1) wherever L(t) is required. Again, as MATLAB indices start from 1, we can use (i-1) wherever an 'i' is occurring in the equation. This would get rid of the requirement to compute f(2) separately.

The code may look like the following:

    L = [1 1.5 0.75 0.125 0 0 0];
    v = 3;
    f2y = zeros(1,2*v);
    for y = 1:v,
      for i = 1:y 
        f2y(2*y) = f2y(2*y)+(-1)^(i-1)*2*L(i)*L(2*y-(i-1)+1) ;    % L((i-1)+1) becomes L(i)
      end
      f2y(2*y) = f2y(2*y) + + (-1)^(y) * L(y+1)^2;
     end

This seems to produce the expected results for the data provided.

[Wilmer]

thank you for the help. the loop works.