Renormalization scheme dependence in the case of a QCD non-power perturbative expansion

A novel, non-power, expansion of QCD quantities replacing the standard perturbative expansion in powers of the renormalized couplant a has recently been introduced and examined by two of us. Being obtained by analytic continuation in the Borel plane, the new expansion functions W_n(a) share the basic analyticity properties with the expanded quantity. In this note we investigate the renormalization scale dependence of finite order sums of this new expansion for the phenomenologically interesting case of the tau-lepton decay rate.