Differentiable, Holomorphic, and Analytic Functions on Complex $\mathrm{\Phi }$-Algebras

Using the notion of order convergent nets, we develop an order-theoretic approach to differentiable functions on Archimedean complex $\mathrm{\Phi }$-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.