Hyperpower series enable the definition of generalized complex analytic functions that extend Goursat's theorem, Liouville's theorem, the identity theorem, and a Paley-Wiener type theorem to generalized holomorphic functions over Robinson-Colombeau numbers.
(2008).Generalized analytic functions on generalized domains[Preprint]
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Complex hyper-power series and generalized complex analytic functions
Hyperpower series enable the definition of generalized complex analytic functions that extend Goursat's theorem, Liouville's theorem, the identity theorem, and a Paley-Wiener type theorem to generalized holomorphic functions over Robinson-Colombeau numbers.