Error bounds for a uniform asymptotic expansion of the Legendre function P_n^-m (cosh z)

For fixed m with m + ½ > 0, an asymptotic expansion for large n is derived for the Legendre function Pn ^-m (cosh z),which is uniformly valid for z in the unbounded interval [0, ∞). Our method is based on an integral representation of this function. The coefficients in the expansion satisfy a recurrence relation. Simple computable bounds are also constructed for the error terms associated with the expansion.