The many limits of mixed means. II: The Carlson sequences
type: Item
instance of: scholarly article
title: The many limits of mixed means. II: The Carlson sequences
zbMATH Open document ID: 0668.40001
DOI: 10.1007/BF01403887
author: John Todd
published in: Numerische Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133300
review text: The sequences introduced by \textit{B. C. Carlson} [Am. Math. Mon. 78, 496-505 (1971; Zbl 0218.65035)] are variants of the Gauss arithmetic geometric sequences. Given (complex) \(a_ 0\), \(b_ 0\) we define \(a_{n+1}=(a_ n+b_ n)\), \(b_{n+1}=\sqrt{(a_ na_{n+1})}\). The main objective of the author is to discuss the convergence and limits of the sequences \(\{a_ n\}\), \(\{b_ n\}\) when the determinations of the square root are made according to an assigned pattern. The original assigned pattern was all positive.
Mathematics Subject Classification ID: 40A05
Mathematics Subject Classification ID: 33E05
Mathematics Subject Classification ID: 65Q05
zbMATH DE Number: 4094075
zbMATH Keywords: Carlson sequences
zbMATH Keywords: Gauss arithmetic geometric sequences
reviewed by: Babban Prasad Mishra
MaRDI profile type: Publication
cites work: Algorithms Involving Arithmetic and Geometric Means
cites work: The arithmetic-geometric mean of Gauss
cites work: Q3329741
cites work: Q5816860
cites work: Q5835647
cites work: Q3290778
description: scientific article; zbMATH DE number 4094075