Polyharmonic functions f of infinite order and type {\tau} on annular regions
are systematically studied. The first main result states that the
Fourier-Laplace coefficients f_{k,l}(r) of a polyharmonic function f of
infinite order and type 0 can be extended to analytic functions on the complex
plane cut along the negative semiaxis. The second main result gives a
constructive procedure via Fourier-Laplace series for the analytic extension of
a polyharmonic function on annular region A(r_{0},r_{1}) of infinite order and
type less than 1/2r_{1} to the kernel of the harmonicity hull of the annular
region. The methods of proof depend on an extensive investigation of Taylor
series with respect to linear differential operators with constant
coefficients.Comment: 32 page