  In this article we review the results of our recent work on the difference
between the Borel representations of tau hadronic spectral function moments
obtained with the CIPT and FOPT methods. For the presentation of the
theoretical results we focus on the large-$\beta_0$ approximation, where all
expressions can be written down in closed form, and we comment on the
generalization to full QCD. The results may explain the discrepancy in the
behavior of the FOPT and CIPT series that has been the topic of intense
discussions in previous literature and which represents a major part of the
theoretical uncertainties in current strong coupling determinations from
hadronic tau decays. The findings also imply that the OPE corrections for FOPT
and CIPT differ and that the OPE corrections for CIPT do not have standard
form.
