Compositional Square Roots of exp(x) and 1+x²

2025/04/28 by Steven R. Finch, Finch, Steven · 2 citations
Mathematics · #26A18 #39-08 #39B12 (Primary) 11B37 #39B22 #65D20 (Secondary) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #General Mathematics (math.GM) #Iterative Methods for Nonlinear Equations #Mathematical Inequalities and Applications #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2504.19999

openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Our work began as an effort to understand calculations by Morris & Szekeres (1961) and Walker (1991) regarding fractional iteration.

Citations

• What do sin(x) and arcsinh(x) have in Common?
• Uniqueness of holomorphic Abel functions at a complex fixed point pair

Cited by

• Fractional Iterates and Oscillatory Convergence
• Exercises in Iterational Asymptotics IV

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