- #1
- 601
- 15
Does anybody know how to prove the following?
[tex]\sum\limits_{n=0}^{\infty} \sum\limits_{m=0}^{\infty} f(n,m) = \sum\limits_{p=0}^{\infty} \sum\limits_{q=0}^{p} f(p,p-q)[/tex]
f(n,m) is any function of n and m.
Note the change of the limiting values on the sums.
[tex]\sum\limits_{n=0}^{\infty} \sum\limits_{m=0}^{\infty} f(n,m) = \sum\limits_{p=0}^{\infty} \sum\limits_{q=0}^{p} f(p,p-q)[/tex]
f(n,m) is any function of n and m.
Note the change of the limiting values on the sums.