Uniform asymptotic expansion of Legendre functions

Leonid Bakaleinikov,Alexander Silbergleit

JOURNAL OF MATHEMATICAL PHYSICS（2020）

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摘要

We find the large number asymptotics of the Legendre functions P-n(cos theta) and Q(n)(cos theta) uniform in 0 <= theta <= pi by reducing the procedure to regular perturbations. The corresponding results for the associated functions P-n(m)(cos theta) and Q(n)(m)(cos theta)are also discussed. Published under license by AIP Publishing.

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关键词

uniform asymptotic expansion,legendre functions

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