Asymptotic Expansion of the Associated Legendre Function Over the Interval $0 \leq \theta \leq \pi$

The associated Legendre function is generally defined by an integral or differential equation. However, a closed-form representation of the associated Legendre function of order 0 or 1 could be beneficial to model the propagation and scattering of waves in spherical coordinates. To this end, an associated Legendre approximation with accuracy over the entire defining interval is presented that is particularly conducive to integral evaluation using stationary phase or steepest descents.