The aim is to provide a method how to decide whether a given
analytic function of $n$ complex variables is linear combination of
finitely many given analytic functions. As coefficients not only constants
are allowed but each coefficient may be an arbitrary analytic function of
specified analytic complex valued functions, the number of which must be
less than $n$ but may vary with the coefficient.
In case it is such a linear combination,
methods to find suitable coefficient functions are given.