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In addition to allowing the introduction of common transcendental functions, power series are shown to behave similar to real power series. Besides being infinitely often differentiable and re-expandable around other points, it is shown that power series satisfy a general intermediate value theorem as well as a maximum theorem and a mean value theorem.
K. Shamseddine, M. Berz, Lecture Notes in Pure and Applied Mathematics 222 (2000) 283-299
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