Error Bounds for a Uniform Asymptotic Expansion of the Legendre Function $Q_n^{ - m} (\cosh z)$
C. L. Frenzen · SIAM Journal on Mathematical Analysis · 1990
For fixed m with $m + \frac{1}{2} > 0$, an asymptotic expansion for large n is obtained for the Legendre function $Q_n^{ - m} (\cosh z)$ that is uniformly valid for z in the unbounded interval $[0,\infty )$. This method is based on an integral representation of the function. The coefficients in the expansion satisfy a recurrence relation, and simple computable bounds are provided for the error terms associated with the expansion.