Convexity and monotonicity for the elliptic integrals of the first kind and applications

An accurate approximation formula for gamma function

“…The following lemma offers a simple criterion to determine the sign of a class of special polynomial on given interval contained in (0, ∞) without using Descartes' Rule of Signs, which play an important role in studying for certain special functions, see for example [30], [31]. A series version can be found in [32].…”