Delta function

The Delta Function

The delta function is defined as follows:

If $m=n$

$\delta _{m,n}=1$

Else if $m\neq n$

$\delta _{m,n}=0$

Example: (The delta function is non-zero only when $m=n$. So, $\alpha _{m}$ is non-zero only when $m=n$. We may then conclude what is stated below.)

$\delta _{m,n}\alpha _{m}=\alpha _{n}$