How do I write this in mathematical symbols: "Result is equal to the sum of product of $a(i)$ and $b(j)$ when $i,j$ are natural numbers and satisfy the property $i+j = k$"?

I forgot to add one more constraint that :

i and j are in the range [0,n] k is in the range [0,2n]

n is a natural number.

Sorry for the late update.

  • $\begingroup$ $\sum\limits_{i+j=k} a_i b_j$ $\endgroup$ – Mher Oct 7 '14 at 14:01

You can note that $j=k-i$ and say $$c(k)=\sum _{i=0}^{k}a(i)b(k-i)$$

  • $\begingroup$ Hi Ross thanks for your answer. It is a really good solution for what I asked but I forgot to add a few constraints to the question. I have updated the Question now. Thanks again. $\endgroup$ – nav_jan Oct 8 '14 at 5:37
  • 1
    $\begingroup$ You can change the indices to reflect that $i=0, j=0$ are allowed as I have done above. If $a(i),b(j)$ are defined to be zero outside the range $[0,n]$ you don't have to do more. If you want, you can put $i, k-i \le n$ below the sum sign to emphasize it. $\endgroup$ – Ross Millikan Oct 8 '14 at 13:15

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