ASYMPTOTIC EXPANSION AND BOUNDS FOR COMPLETE ELLIPTIC INTEGRALS

摘要

In the article, we present several new bounds for the the complete elliptic integrals K(r) = -integral(pi/2)(0)(1-r(2) sin(2)theta)(-1/2)d theta and E(r) = -integral(pi/2)(0)(1-r(2) sin(2)theta)(1/2)d theta, and find an asymptotic expansion for K(r) as r -> 1, which are the refinements and improvements of the previously well-known results.