Abstract
By studying the monotonicity properties of K(r), E(r) and some combinations of elementary functions and special functions, some new inequalities for the complete elliptic integrals of the first and second kinds are established. where K(r) =??/2 0 (1 ? r2 sin2?)?1/2d?, E(r)=??/2 0 (1 ? r2 sin2?)1/2d? denote the complete elliptic integrals of the first and second kind, r ? (0,1).
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