Elementary Proof that the Arithmetic Mean of any number of Positive Quantities is greater than the Geometric Mean

The Arithmetic - Geometric Mean and Fast Computation of Elementary Functions

We produce a self contained account of the relationship between the Gaussian arithmetic-geometric mean iteration and the fast computation of elementary functions. A particularly pleasant algorithm for r is one of the by-products.

Is There any Mean to Postpone The Menopausal Ovarian Senescence?

The ovarian reserve (OR) gradually decreases throughout the female fertile life. This continuous depletion in OR is irreversible. This occurs through a programmed cell death known apoptosis. Some factors hasten such depletion such as chemo- and radiotherapy. Others have been investigated in trials to preserve the OR including gonadotropins, cytokines, growth hormones, nitric oxide and reorganiz...

Generalizing the Arithmetic Geometric Mean

The paper discusses the asymptotic behavior of generalizations of the Gauss’s arithmetic-geometric mean, associated with the names Meissel (1875) and Borchardt (1876). The "hapless computer experiment" in the title refers to the fact that the author at an earlier stage thought that one had genuine asymptotic formulae but it is now shown that in general "fluctuations" are present. However, no ve...

The matrix arithmetic-geometric mean inequality revisited

An Alternative and United Proof of a Double Inequality for Bounding the Arithmetic-geometric Mean

For more information on the arithmetic-geometric mean and the complete elliptic integral of the first kind, please refer to [2, pp. 132–136], [4] and related references therein. In [4, Theorem 4] and [6], it was proved that the inequality M(a, b) ≥ L(a, b) (5) holds true for positive numbers a and b and that the inequality (5) becomes equality if and only if a = b, where L(a, b) = b− a ln b− ln...