Asymptotic Approximations for Symmetric Elliptic Integrals

  title={Asymptotic Approximations for Symmetric Elliptic Integrals},
  author={B. C. Carlson and John L. Gustafson},
Abstract. Symmetric elliptic integrals, which have been used as replacements for Legendre’s integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than the others, asymptotic approximations with error bounds are presented. In most cases they are derived from a uniform approximation to the integrand. As an application the symmetric elliptic integrals of the first, second, and third kinds are proved… CONTINUE READING

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