Roelands, M.Schwanke, Christopher2024-08-072024-08-072025-01Roelands, M. & Schwanke, C. 2025, 'Differentiable, holomorphic, and analytic functions on complex Φ-algebras', Journal of Mathematical Analysis and Applications, vol. 541, no. 1, art. 128671, pp. 1-26, doi : 10.1016/j.jmaa.2024.128671.0022-247X (print)1096-0813 (online)10.1016/j.jmaa.2024.128671http://hdl.handle.net/2263/97473Using the notion of order convergent nets, we develop an order-theoretic approach to differentiable functions on Archimedean complex Φ-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.en© 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC license.DifferentiationComplex vector latticeAnalytic functionHolomorphic functionArticle