  In this paper we show that, as in the spacelike case, the inverse logarithmic
expansion is applicable for all values of the argument of the analytic coupling
constant. We present two different approaches, one of which is based primarily
on trigonometric functions, and the latter is based on dispersion integrals.
  The results obtained up to the 5th order of perturbation theory, have a
compact form and their acquiring is much easier than the methods that have been
used before. As an example, we apply our results to study the Higgs boson decay
into a bb pair.
