منابع مشابه
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...
متن کاملAn Arithmetic and Geometric Mean Invariant
A positive real interval, [a, b] can be partitioned into sub-intervals such that sub-interval widths divided by sub-interval ”‘average”’ values remains constant. That both Arithmetic Mean and Geometric Mean ”‘average”’ values produce constant ratios for the same log scale is the stated invariance proved in this short note. The continuous analog is briefly considered and shown to have similar pr...
متن کاملSome remarks on the arithmetic-geometric index
Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.
متن کاملOn Inequalities for Hypergeometric Analogues of the Arithmetic-geometric Mean
In this note, we present sharp inequalities relating hypergeometric analogues of the arithmetic-geometric mean discussed in [5] and the power mean. The main result generalizes the corresponding sharp inequality for the arithmetic-geometric mean established in [10].
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ژورنال
عنوان ژورنال: Topology
سال: 1991
ISSN: 0040-9383
DOI: 10.1016/0040-9383(91)90004-n