Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity
نویسندگان
چکیده
منابع مشابه
Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity
We find two convergent series expansions for Legendre’s first incomplete elliptic integral F (λ, k) in terms of recursively computed elementary functions. Both expansions are valid at every point of the unit square 0 < λ, k < 1. Truncated expansions yield asymptotic approximations for F (λ, k) as λ and/or k tend to unity, including the case when logarithmic singularity λ = k = 1 is approached f...
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متن کاملEvaluation of an Integral Arising in Numerical Integration Near a Logarithmic Singularity
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2007
ISSN: 0377-0427
DOI: 10.1016/j.cam.2006.04.053