Use while loop in equation

I need to calculate a values c2, c3, c4,..., using the equation:

where alpha and beta are the elements of a given vectors of length k. For each q i need to calculate the result. usually Cq will result zero, so i need to find what value of q will be different to zero. I think to do that thing in matlab is using while, but my problem is combine summatory and while in matlab.

for example

in this case the value of k is 2, aplying the equation above for each c2=c3=c4=0 except in c5 which means q=5, by the way values of q start from 2 and above.

Please help me.

[Walter Roberson]

When do you stop? What is the upper limit for q? Is it expected that once a particular q generates 0 that all higher ones will too?

When you say 0, is that that the terms are literally identical value, or is that a 0 to within some numeric precision? For large enough q the multiplications by j^q are going to result in loss of precision it appears to me, so numeric 0 rather than algebraic 0 would make more sense to me.

[JORGE ORDOÑEZ CARRASCO]

As you can see q starts from 2. In this equation above I need to break the calculation when cq results different to zero. Which implies a value of q not bigger than 100 or 1000 for example in given exercise with a two vector the value of q is five and cq is not zero.

[David Hill]

You should be able to easily modify my answer to match your indexing.

[JORGE ORDOÑEZ CARRASCO]

I need to break the calculation when a cq is different to zero. I was thinking to use a while loop, to break the calculation when a cq is different to zero. I can use so sum((1:k) expression) inside the while I don’t know maybe can work. Thanks

Answer 1

[David Hill]

C=@(q)sum((1:k).^q.*alpha)/factorial(q)-sum((1:k).^(q-1).*beta)/factorial(q-1);
q=1:100;
c=arrayfun(@(x)C(x),q);
plot(q,c);

[JORGE ORDOÑEZ CARRASCO]

Nice clue