Bracken, P. An arithmetic-geometric mean inequality. (English) Zbl 1135.26302 Expo. Math. 19, No. 3, 273-279 (2001). Summary: Several integrals which are related to the arithmetic-geometric mean are developed and proved in a very elementary way. These results can be used to prove a known inequality which relates this mean to the logarithmic mean. Cited in 12 Documents MSC: 26D15 Inequalities for sums, series and integrals 26E60 Means PDF BibTeX XML Cite \textit{P. Bracken}, Expo. Math. 19, No. 3, 273--279 (2001; Zbl 1135.26302) Full Text: DOI References: [1] Gauss, C. F., Werke, Vol. 3 (1866-1933), Göttingen [2] Salamin, E., Computation of \(π\) using the arithmetic-geometric mean, Math. Comp., 30, 565-570 (1976) · Zbl 0345.10003 [3] Carlson, B. C.; Vuorinen, M., Siam Review, Problem 91-17, 34, 653 (1992) [4] Vananamurthy, M. K.; Vuorinen, M., Inequalities of Means, J. of Mathematical Analysis and Applications, 183, 155-166 (1994) · Zbl 0802.26009 [5] Borwein, J. M.; Borwein, P. B., PI and the AGM- A Study in Analytic Number Theory and Computational Complexity (1987), John Wiley · Zbl 0611.10001 [6] Almkvist, G.; Berndt, B., Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses, \(π\), and the Ladies Diary, Amer. Math. Monthly, 95, 585-607 (1988) · Zbl 0665.26007 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.