A Derivative Conjecture (Open)

Summary: The authors study the asymptotic rate of convergence of the sequence ($z_1 = a, z_{n+1} = a^{z_n}$ for all $n \ge 1$). A precise characterization of the rate is conjectured for the sublinear case.

Classification: Primary, Classical Analysis; Secondary, Special Functions

Fuchang Gao
Department of Mathematics
University of Idaho
Moscow, ID 83844
Email: fuchang@uidaho.edu

Lixing Han
Department of Mathematics
University of Michigan-Flint
Flint, MI 48502
Email: lxhan@umflint.edu

Kenneth Schilling
Department of Mathematics
University of Michigan-Flint
Flint, MI 48502
Email: ksch@umflint.edu

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