  We introduce matching functions as a means of summing heavy-quark logarithms
to any order. Our analysis is based on Witten's approach, where heavy quarks
are decoupled one at a time in a mass-independent renormalization scheme. The
outcome is a generalization of the matching conditions of Bernreuther and
Wetzel: we show how to derive closed formulas for summed logarithms to any
order, and present explicit expressions for leading order and next-to-leading
order contributions. The decoupling of heavy quarks in theories lacking
asymptotic freedom is also considered.
