The paper is concerned with linear differential equations, essentiallywhereof order 2nfor holomorphic functionsuof 2ncomplex variableswe derive power series expansions for the generating functions for mtegral operators of generalized Vekua's and Bergman's type (called Ricmann function and Bergman kernel respectively). which permit integral representations of the solutionsu. In case of the above mentioned equation these generating functions are shown to be associated by complex iontegrat transformations.