When series of computable functions with varying domains are computable

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Mathematical Logic Quarterly 59 (6):471-493 (2013)
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10.1002/malq.201200053

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On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
Nicht konstruktiv beweisbare sätze der analysis.Ernst Specker - 1949 - Journal of Symbolic Logic 14 (3):145-158.
Notes on constructive mathematics.Per Martin-Löf - 1970 - Stockholm,: Almqvist & Wiksell.
On the Definition of Computable Function of a Real Variable.J. C. Shepherdson - 1976 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):391-402.

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