  We present a special solutions of the discrete Painlev\'e equations
associated with $A_0^{(1)}$, $A_0^{(1)*}$ and $A_0^{(1)**}$-surface. These
solutions can be expressed by solutions of linear difference equations. Here
the $A_0^{(1)}$-surface discrete Painlev\'e equation is the most generic
difference equation, as all discrete Painlev\'e equations can be obtained by
its degeneration limit. These special solutions exist when the parameters of
the discrete Painlev\'e equation satisfy a particular constraint. We consider
that these special functions belong to the hypergeometric family although they
seems to go beyond the known discrete and $q$-discrete hypergeometric
functions. We also discuss the degeneration scheme of these solutions.
