  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 to be linearly independent with respect to
coefficients that are rational functions.
