Delta function

The Delta Function

The delta function is defined as follows:

If $m=n$

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

Else if $m\ne n$

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

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.)

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