Taylor Expansion for an Analytic Hypersurface in R N

Here we obtain a Taylor’s expansion of the function ρ(x, r) = |B(x,r)| |B(x,r)∩Ω| for r small and x ∈ ∂Ω where the boundary of domain Ω is assumed to be analytic. The coefficients are expressed as recurrence relation and it is proved yhat the series is odd.