  Polymer models play the special role of elucidating the elementary features
describing the physics of long molecules and become essential to interpret the
measurements of their magnitudes. In this work the end-to-end distance of an
extensible discrete worm-like chain polymer as a function of the applied force
has been calculated both numerically and analytically, the latter as an
effective approximation. The numerical evaluation uses the Transfer Matrix
formalism to obtain an exact calculation of the partition function, while the
analytic derivations generalize the simple phenomenological formulas largely
used up to now. The obtained formulas are simple enough to be implemented in
the fit analysis of experimental data of semi-flexible extensible polymers,
with the result that the elastic parameters obtained are compatible with
previous measurements, and more, their accuracy strongly improves in a large
range of chain extensibility.
