We give the explicit formulas of the reproducing kernels of the space of harmonic polynomials of $\mathfrak{p} \subset \mathfrak{g} $ in the case of classical real rank 1, which are generalizations of the well-known reproducing formulas of classical harmonic polynomials on the unit sphere or any other $SO(p)$-orbits in $\mathbf{C}^p$. These formulas are expressed as integrals on a single orbit, simplifying our previous results that are expressed as double integrals on some family of nilpotent orbits.