Series expansions for the third incomplete elliptic integral via partial fraction decompositions

[摘要] We find convergent double series expansions for Legendre's third incomplete elliptic integral valid in overlapping subdomains of the unit square. Truncated expansions provide asymptotic approximations in the neighborhood of the logarithmic singularity (1, 1) if one of the variables approaches this point faster than the other. Each approximation is accompanied by an error bound. (C) 2006 Elsevier B.V. All rights reserved.

[发布日期] 2007-10-15

[效力级别]  Proceedings Paper

[关键词] incomplete elliptic integral;series expansion;asymptotic approximation;partial fraction decomposition