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The many limits of mixed means

Authors:

John Todd

Affiliation:

1. California Institute of Technology, 91125, Pasadena, CA, USA

Abstract:

The sequences introduced by Carlson (1971) are variants of the Gauss arithmetic geometric sequences (which have been elegantly discussed by D. A. Cox (1984, 1985)). Given (complex)a₀,b₀ we define

$a_{n + 1} : = tfrac{1}{2}(a_n + b_n ),b_{n + 1} : = sqrt {(a_n a_{n + 1} )}$

Keywords:	KeywordHeading" >Subject Classifications AMS(MOS): 40A05, 33A25, 65Q05 CR: F.2.m, G.1.m
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