Uniform asymptotic expansions of symmetric elliptic integrals

Symmetric standard elliptic integrals are considered when two or more param eters are larger than the others. The distributional approach is used to de rive seven expansions of these integrals in inverse powers of the asymptoti c parameters. Some of these expansions also involve logarithmic terms in th e 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 para meters than the original integrals. The coefficients of the seventh expansi on again involve elliptic integrals, but with less parameters than the orig inal integrals. The convergence speed of any of these expansions increases for an increasing difference between the asymptotic variables and the remai ning ones. All the expansions are accompanied by an error bound at any orde r of the approximation.