Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Uniform computational complexity of Taylor series
14th International Colloquium on Automata, languages and programming
Complexity theory of real functions
Complexity theory of real functions
Complexity and real computation
Complexity and real computation
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
Computability and continuity on the real arithmetic hierarchy and the power of type-2 nondeterminism
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
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We present results concerning analytic machines, a model of real computation introduced by Hotz which extends the well known Blum, Shub and Smale machines by infinite converging computations. We use the machine model to define computability of complex analytic (i.e. holomorphic) functions and examine in particular the class of analytic functions which have analytically computable power series expansions. We show that this class is closed under the basic analytic operations composition, local inversion and analytic continuation.