Generalizing the arithmatic geometric mean — a hapless computer experiment

Jaak Peetre

International Journal of Mathematics and Mathematical Sciences, 1989, vol. 12, 1-11

Abstract:

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 very conclusive results are obtained so the paper ends in a conjecture concerning the special rôle of the algorithms of Gauss and Borchardt. 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 very conclusive results are obtained so the paper ends in a conjecture concerning the special rôle of the algorithms of Gauss and Borchardt.

Date: 1989
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/12/567583.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/12/567583.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:567583

DOI: 10.1155/S016117128900027X

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().