The many limits of mixed means. II: The Carlson sequences
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.
scientific article; zbMATH DE number 4094075