  The relation between force and stretch in the worm-like chain model of
entropic elasticity is examined. Although no closed-form expression is valid
for all values of forcing, solutions in the form of asymptotic series can be
obtained under conditions of small and large applied force. The small and large
stretch limits correspond to regular and boundary layer perturbation problems,
respectively. The perturbation problems are solved and series solutions
obtained for force as a function of stretch. The form of the asymptotic series
suggest a uniform approximation valid for all stretch that is an improvement on
existing approximations.
