Abstract
In this paper, we obtain a new simple rational approximation for Ka(r): the inequality 2Ka(r)/π>g2r′/g1r′ holds for all r∈(0,1), where Ka(r) is the generalized elliptic integral of the first kind, r′=1−r2, g1r′ and g2r′ are specific primary and quadratic polynomials about r′, respectively. In particular, when a is taken as 1/2, 1/3, 1/4, 1/5 and 1/6 respectively, we can obtain some new specific lower bounds of the corresponding functions.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)