Here we obtain a Taylor’s expansion of the function $\rho(x,r) = \frac{|B(x,r)|}{|B(x,r) \cap \Omega|}$ for $r$ small and $x \in \partial \Omega$ where the boundary of domain $\Omega$ is assumed to be analytic. The coefficients are expressed as recurrence relation and it is proved yhat the series is odd.