Quadratically converging rational mean iterations

DOI10.1016/0022-247X(91)90043-YzbMath0727.26008MaRDI QIDQ803301

Peter B. Borwein

Publication date: 1991

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

algebraic differential equationsmultipliersquadratic convergencetheta functionsorder of convergenceelliptic integralsarithmetic-geometric mean,hypertranscendental functionsmean iterationsuniformizing parameters

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Iteration of real functions in one variable (26A18) Multiple sequences and series (40B05) Representation and superposition of functions (26B40) Elliptic integrals as hypergeometric functions (33C75) Convergence and divergence of infinite products (40A20)

Cites Work

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• A class of hypertranscendental functions
• From geometry to Euler identities
• Remarks on a paper by W. Schwarz
• On the compounding of certain means
• On an algorithm considered by Stieltjes
• The Way of All Means
• Hypertranscendence of the Functional Equation g(x 2 ) = [ g(x) 2 + cx]
• [https://portal.mardi4nfdi.de/wiki/Publication:3829784 On the Mean Iteration (a, b) ← � � a+3b 4 , √ab+b 2 � �]

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