Composed Padé-type approximation

We introduce Padé-type (and Padé) approximation to complex-valued harmonic functions in the unit disk D. This coordinate approximation is defined to be a composed Padé-type approximation (respectively, a composed Padé approximation). The basic properties of such an approximation are being studied and we are showing that any classical Padé-type approximant to an analytic function on D coincides with a composed Padé-type approximant to this function.