  Following Osipov and Hiller, a generalized heat kernel expansion is
considered for the effective action of bosonic operators. In this
generalization, the standard heat kernel expansion, which counts inverse powers
of a c-number mass parameter, is extended by allowing the mass to be a matrix
in flavor space. We show that the generalized heat kernel coefficients can be
related to the standard ones in a simple way. This holds with or without trace
and integration over spacetime, to all orders and for general flavor spaces.
Gauge invariance is manifest.
