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

Authors:
D. Karp;A. Savenkova;S. M. Sitnik
Affiliations:
Institute of Applied Mathematics, 7 Radio St., Vladivostok, 690041, Russia;Institute of Applied Mathematics, 7 Radio St., Vladivostok, 690041, Russia;Voronezh Institute of the Ministry of Internal Affairs of the Russian Federation, Russia
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 3
Cited 2

Asymptotic approximations for symmetric elliptic integrals

SIAM Journal on Mathematical Analysis - Special issue: the articles in this issue are dedicated to Richard Askey and Frank Olver
Asymptotic expansions of symmetric standard elliptic integrals

SIAM Journal on Mathematical Analysis
Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity

Journal of Computational and Applied Mathematics

Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity

Journal of Computational and Applied Mathematics
Periodic solutions of a derivative nonlinear Schrödinger equation: Elliptic integrals of the third kind

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

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.