Asymptotic Approximations for Symmetric Elliptic Integrals

DOI10.1137/S0036141092228477zbMath0794.41021arXivmath/9310223OpenAlexW1982792721MaRDI QIDQ4292633

John L. Gustafson, B. C. Carlson

Publication date: 15 August 1994

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9310223

zbMATH Keywords

asymptotic approximationssymmetric elliptic integrals

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Inequalities for sums, series and integrals (26D15) Elliptic functions and integrals (33E05) Other analytical inequalities (26D20)

Related Items (16)

Inequalities and bounds for elliptic integrals ⋮ Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity ⋮ Series expansions for the third incomplete elliptic integral via partial fraction decompositions ⋮ An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions ⋮ Bounds for symmetric elliptic integrals. ⋮ A new upper bound for the complete elliptic integral of the first kind ⋮ Convergent expansions and bounds for the incomplete elliptic integral of the second kind near the logarithmic singularity ⋮ Inequalities for Gaussian hypergeometric functions ⋮ Series expansions of symmetric elliptic integrals ⋮ Uniform approximations of the first symmetric elliptic integral in terms of elementary functions ⋮ Monotonicity theorems and inequalities for the complete elliptic integrals ⋮ High accuracy complete elliptic integrals for solving the Hertzian elliptical contact problems ⋮ An upper bound for the logarithmic capacity of two intervals ⋮ On a function involving generalized complete \((p, q)\)-elliptic integrals ⋮ Symmetric standard elliptic integrals with two or three large parameters ⋮ Note on certain inequalities for Neuman means

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