Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, &pgr;, and the Ladies Diary
American Mathematical Monthly
Close-to-convexity properties of Gaussian hypergeometric functions
Journal of Computational and Applied Mathematics
An inequality involving the generalized hypergeometric function and the arc length of an ellipse
SIAM Journal on Mathematical Analysis
Monotonicity theorems and inequalities for the complete elliptic integrals
Journal of Computational and Applied Mathematics
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In this paper, we present several bounds for the perimeter of an ellipse, which improve some well-known results.