Asymptotic formulas for elliptic integrals

Abstract

<p>Asymptotic formulas are derived for incomplete elliptic integrals of all three kinds when the arguments are real and tend to infinity or to zero. Practical error bounds are found for the asymptotic formulas. Several techniques are used, including a method recently discovered by R. Wong for finding asymptotic expansions with remainder terms for integral transforms. Most of the asymptotic formulas and all of the error bounds appear to be new;We use incomplete elliptic integrals which possess a high degree of permutation symmetry in the function arguments. The asymptotic formulas are applicable to complete elliptic integrals as a special case; some of the error bounds are treated separately in the complete case;Numerical examples are given to demonstrate the typicalaccuracy which can be expected from the formulas, as well as the;closeness of the error bounds;*DOE Report IS-T-1014. This work was performed under ContractNo. W-7405-Eng-82 with the U.S. Department of Energy.</p>