In the article, we present several new bounds for the the complete elliptic integrals K (r) = | 0π /2(1−r2 sin2 θ )−1/2dθ and E (r) = | 0π /2 (1−r2 sin2 θ )1/2dθ , and find an asymptotic expansion for K (r) as r → 1, which are the refinements and improvements of the previously well-known results. © 2020 ...
