  The electroelastic 4 $\times$ 4 Green's function of a piezoelectric hexagonal
(transversely isotropic) infinitely extended medium is calculated explicitly in
closed compact form (eqs. (73) ff. and (88) ff., respectively) by using residue
calculation. The results can also be derived from Fredholm's method [2]. In the
case of vanishing piezoelectric coupling the derived Green's function coincides
with two well known results: Kr{\"o}ner 's expressions for the elastic Green's
function tensor [4] is reproduced and the electric part then coincides with the
electric potential (solution of Poisson equation) which is caused by a unit
point charge. The obtained electroelastic Green's function is useful for the
calculation of the electroelastic Eshelby tensor [16].
