  Based on the full similarity in algebraic properties and differentiation
rules between quaternionic (H-) holomorphic and complex (C-) holomorphic
functions, we assume that there exists one holistic notion of a holomorphic
function that has a H-representation in the case of quaternions and a
C-representation in the case of complex variables. We get the essential
definitions and criteria for a quaternionic power series convergence, adapting
complex analogues to the quaternion case. It is established that the power
series expansions of any holomorphic function in C- and H-representations are
similar and converge with identical convergence radiuses. We define a
H-analytic function and prove that every H-holomorphic function is H-analytic.
Some examples of power series expansions are given.
