# Products of Kronecker Deltas

1. Jun 1, 2012

### anthony2005

Please, can some one tell me how to simplify this expression resolving the deltas

$\sum_{i_{1}+i_{2}+...i_{n}=k} f_{i_{1}}f_{i_{2}}...f_{i_{n}} \prod_{j=1}^{m}\delta_{a_{j1}i_{1}+...a_{jn}i_{n}-\rho_{j}}$

where all $a_{j1},..a_{jn}$ and $\rho_{j}$ are integers. Each $i_{1},..,i_{n}$ range from 0 to k, and the delta is Kronecker (its argument must be null).

After resolving the deltas I guess one would have a sum of the $f$s in the form $f_{g\left(a_{ij},\rho_{j},k,m\right)}$ where g is a function of those arguments.