connection with the standard Dirac representation of by writing and

which makes clear the recovery of the delta as an infinite bandwidth limit of the integral.

Summation

All sums in this section refer to the unnormalized sinc function.

The sum of over integer from 1 to equals :

The sum of the squares also equals :

When the signs of the addends alternate and begin with +, the sum equals :

The alternating sums of the squares and cubes also equal :

Series expansion