Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity

Authors:
D. Karp;S. M. Sitnik
Affiliations:
Institute of Applied Mathematics, Vladivostok, Russia;Voronezh Institute of the Ministry of Internal Affairs of the Russian Federation
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

We find two convergent series expansions for Legendre's first incomplete elliptic integral F(@l,k) in terms of recursively computed elementary functions. Both expansions are valid at every point of the unit square 0