  We introduce a new product formula which combines an orthogonal projection
with a complex function of a non-negative operator. Under certain assumptions
on the complex function the strong convergence of the product formula is shown.
Under more restrictive assumptions even operator-norm convergence is verified.
The mentioned formula can be used to describe Zeno dynamics in the situation
when the usual non-decay measurement is replaced by a particular generalized
observables in the sense of Davies.
