  We identify a class of hyperbolic transcendental entire maps and we prove
that some of its elements generate a class of potentials for which exhibit a
conformal and invariant probability Gibbs measure. The methods and techniques
from the thermodynamic formalism can be extended to this class of potentials.
To complement this study we highlight that the dynamics of such a map on some
subset of the Julia set is conjugated to the shift map over a code space with
countable alphabet and the euclidean metric on the complex plane induces a
metric on the symbolic space which is not compatible with the shift standard
metric. From this fact, we provide a general description of the thermodynamic
formalism from symbolic dynamic outlook, by studying the shift map acting on a
non-compact and invariant subset of the full shift space with a countably
infinite alphabet and a class of weakly H\"older continuous potentials, to
prove the existence of a conformal and absolutely continuous invariant
probability measure.
