  This paper investigates the expected number of complex roots of nonlinear
equations. Those equations are assumed to be analytic, and to belong to certain
inner product spaces. Those spaces are then endowed with the Gaussian
probability distribution.
  The root count on a given domain is proved to be `additive' with respect to a
product operation of functional spaces. This allows to deduce a general theorem
relating the expected number of roots for unmixed and mixed systems. Examples
of root counts for equations that are not polynomials nor exponential sums are
given at the end.
