Differentiable, holomorphic, and analytic functions on complex Φ-algebras

Using the notion of order convergent nets, we develop an order-theoretic approach to differentiable functions on Archimedean complex Phi-algebras. Most notably, we improve the Cauchy-Hadamard formulas for universally complete complex vector lattices given by both authors in a previous paper in order to prove that analytic functions are holomorphic in this abstract setting. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC license (http://creativecommons .org /licenses /by -nc /4 .0/).