Carlson, B. C.; Gustafson, J. L. Asymptotic approximations for symmetric elliptic integrals. (English) Zbl 0794.41021 SIAM J. Math. Anal. 25, No. 2, 288-303 (1994). Symmetric elliptic integrals are homogeneous functions of three or four variables. When some of the variables are much larger than the others, asymptotic approximations to them are given with error bounds. Further, the symmetric elliptic integrals of the first, second, and third kinds are proved to be linearly independent with respect to coefficients that are rational functions. Reviewer: Y.Kobayashi (Tottori) Cited in 3 ReviewsCited in 16 Documents MSC: 41A50 Best approximation, Chebyshev systems 33E05 Elliptic functions and integrals 26D15 Inequalities for sums, series and integrals 26D20 Other analytical inequalities Keywords:symmetric elliptic integrals; asymptotic approximations PDFBibTeX XMLCite \textit{B. C. Carlson} and \textit{J. L. Gustafson}, SIAM J. Math. Anal. 25, No. 2, 288--303 (1994; Zbl 0794.41021) Full Text: DOI arXiv Digital Library of Mathematical Functions: §19.12 Asymptotic Approximations ‣ Legendre’s Integrals ‣ Chapter 19 Elliptic Integrals §19.27(iii) 𝑅_𝐺(𝑥,𝑦,𝑧) ‣ §19.27 Asymptotic Approximations and Expansions ‣ Symmetric Integrals ‣ Chapter 19 Elliptic Integrals §19.27(ii) 𝑅_𝐹(𝑥,𝑦,𝑧) ‣ §19.27 Asymptotic Approximations and Expansions ‣ Symmetric Integrals ‣ Chapter 19 Elliptic Integrals §19.27(iv) 𝑅_𝐷(𝑥,𝑦,𝑧) ‣ §19.27 Asymptotic Approximations and Expansions ‣ Symmetric Integrals ‣ Chapter 19 Elliptic Integrals §19.27(v) 𝑅_𝐽(𝑥,𝑦,𝑧,𝑝) ‣ §19.27 Asymptotic Approximations and Expansions ‣ Symmetric Integrals ‣ Chapter 19 Elliptic Integrals §19.27(vi) Asymptotic Expansions ‣ §19.27 Asymptotic Approximations and Expansions ‣ Symmetric Integrals ‣ Chapter 19 Elliptic Integrals