  We perform an all-orders resummation of the QCD Adler D-function for the
vector correlator, in which the portion of perturbative coefficients involving
the leading power of b, the first beta-function coefficient, is resummed. To
avoid a renormalization scale dependence when we match the resummation to the
exactly known NLO and NNLO results, we employ the Complete Renormalization
Group Improvement (CORGI) approach. These fixed-order and resummed CORGI
results are analytically continued by numerically performing a contour integral
to obtain corresponding fixed and all-orders ``contour-improved'' results for
the e+e- R-ratio ands its tau decay analogue R_{\tau}. The difference between
these fixed-order and all-order results is used to estimate the uncertainty in
the extraction of {alpha}_{s}({M}_{Z}^{2}} from R_{\tau} measurements, and that
in the QED coupling {\alpha}({M}_{Z}^{2}) due to hadronic corrections related
to R. Analogous resummations for the scalar correlator are performed, and used
to assess the uncertainty in the Higgs decay width to a heavy quark pair. We
point out that CORGI fixed-order contour-improved results for R and the Higgs
decay width, can be given explicitly in terms of the Lambert-W function and
hypergeometric functions, avoiding the need for numerical integration.
