satisfies the equation and behaves like a delta function at

Plugging the Green's function into the canonical diffusion equation,
Eq. 16, gives on both sides

verifying that it is a solution to the equation.

As , for , the argument of the exponent goes
to , and
. For *z*=*z*', it goes to infinity
as
. The integral over *z*' can be found by
substituting
and gives

showing that it is correctly normalized to be the solution for a delta function source or point source at