A Remark on Holomorphic Functions Rational in Some Variables

Considering the holomorphic functions in a polycylindrical domain which are rational in someof the variables for the arbitrary fixed values of other variables, we prove thatthe functions are representable as a ratio of polynomials in these variables whose coefficientsare holomorphic in the remaining variables. We use the Kronecker method for establishing somecriterion for the rationality of a holomorphic function of one complex variable ina neighborhood of zero by using the properties of Hankel matrices.