  In this paper, we present a new approach to the discrete version of the
Wormlike Chain Model (WCM) of semiflexible polymers. Our solution to the model
is based on a new computational technique called the Generalized Borel
Transform (GBT) which we use to study the statistical mechanics of semiflexible
polymer chains. Specifically, we evaluate the characteristic function of the
model approximately. Afterward, we compute the polymer propagator of the model
using the GBT and find an expression valid for polymers with any number of
segments and values of the semiflexibility parameter. This expression captures
the limits of flexible and infinitely stiff polymers exactly. In between, a
smooth and approximate crossover behavior is predicted. Another property of our
propagator is that it fulfills the condition of finite extensibility of the
polymer chain. We have also calculated the single chain structure factor. This
property is a decreasing function of the wave vector, $k,$ until a plateau is
reached. Our computations clearly show that the structure factor decreases
faster with increasing wave vector when the semiflexibility parameter is
increased. Furthermore, when the wave vector is large enough, there is a regime
where the structure factor follows an approximate power law of the form
$k^{-\theta}$ even for short polymer chains. $\theta$ is equal to two for
flexible polymers and to one for rigid chains. We also compare our results to
the predictions of other models.
