Constructive Approximation

, Volume 17, Issue 4, pp 535–559 | Cite as

Uniform Asymptotic Expansions of Symmetric Elliptic Integrals

  • J. L. López
Article

Abstract.

Symmetric standard elliptic integrals are considered when two or more parameters are larger than the others. The distributional approach is used to derive seven expansions of these integrals in inverse powers of the asymptotic parameters. Some of these expansions also involve logarithmic terms in the asymptotic variables. These expansions are uniformly convergent when the asymptotic parameters are greater than the remaining ones. The coefficients of six of these expansions involve hypergeometric functions with less parameters than the original integrals. The coefficients of the seventh expansion again involve elliptic integrals, but with less parameters than the original integrals. The convergence speed of any of these expansions increases for an increasing difference between the asymptotic variables and the remaining ones. All the expansions are accompanied by an error bound at any order of the approximation.

Key words. Elliptic integrals, Uniform asymptotic expansions, Distributional approach. AMS Classification. 41A60, 33E05. 

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Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • J. L. López
    • 1
  1. 1.Departamento de Matemática e Informática Universidad Pública de Navarra 31006-Pamplona Spain jl.lopez@unavarra.esES

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