  In order to estimate the effects of local structure on the Hubble parameter
we calculate the low-redshift expansion for $H(z)$ and $\frac{\delta H}{H}$ for
an observer at the center of a spherically symmetric matter distribution in
presence of a cosmological constant. We then test the accuracy of the formulae
comparing them with fully relativistic non perturbative numerical calculations
for different cases for the density profile. The low red-shift expansion we
obtain gives results more precise than perturbation theory since is based on
the use of an exact solution of Einstein's field equations. For larger density
contrasts the low red-shift formulae accuracy improves respect to the
perturbation theory accuracy because the latter is based on the assumption of a
small density contrast, while the former does not rely on such assumption.
  The formulae can be used to take into account the effects on the Hubble
expansion parameter due to the monopole component of the local structure. If
the $H(z)$ observations will show deviations from the $\Lambda CDM$ prediction
compatible with the formulae we have derived, this could be considered an
independent evidence of the existence of a local inhomogeneity, and the
formulae could be used to determine the characteristics of this local
structure.
