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Error bounds for a uniform asymptotic expansion of the Legendre function Q n -m (coshz). (English) Zbl 0688.41034
Summary: For fixed m with m+>0, an asymptotic expansion for large n is obtained for the Legendre function Q n -m (coshz) that is uniformly valid for z in the unbounded interval [0,). 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.
MSC:
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
33C55Spherical harmonics