An analytic approach to the Collatz \(3n+1\) problem for negative start values

DOI10.1007/s40315-013-0017-zzbMath1329.11011OpenAlexW2461014525MaRDI QIDQ380718

Gerhard Opfer, Lothar Berg

Publication date: 14 November 2013

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40315-013-0017-z

zbMATH Keywords

\(3n-1\) problemCollatz \(3n+1\) problem for negative start valueslinear operators acting on holomorphic functionsnatural boundary

Mathematics Subject Classification ID

Recurrences (11B37) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Special sequences and polynomials (11B83) Functional equations for complex functions (39B32) Systems of functional equations and inequalities (39B72)

Related Items (1)

3x+1 inverse orbit generating functions almost always have natural boundaries

Cites Work

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• Functional equations connected with the Collatz problem
• The dynamical system generated by the \(3n+1\) function
• On the "3x + 1" Problem
• Don't Try to Solve These Problems
• On Converse Gap Theorems
• Note on the Converse of Fabry's Gap Theorem
• On the \(3n+1\) problem

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