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Zbl 0688.41034
Frenzen, C.L.
Error bounds for a uniform asymptotic expansion of the Legendre function $Q\sb n\sp{-m}(\cosh \,z)$. (English)
[J] SIAM J. Math. Anal. 21, No.2, 523-535 (1990). ISSN 0036-1410; ISSN 1095-7154/e

Summary: For fixed m with $m+>0$, an asymptotic expansion for large n is obtained for the Legendre function $Q\sb n\sp{-m}(\cosh z)$ 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.

MSC 2000:: *41A60 Asymptotic problems in approximation
33C55 Elliptic integrals as hypergeometric functions

Keywords: error bound; uniform asymptotic expansion; Legendre function; integral representation

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