John Myhill gives gave an example of a recursive function defined on a compact interval and having a continuous derivative that is not recursive [Michigan Math. J. 18 (1971), 97-98, MR0280373]. However, Pour-El and Richards have shown that if a recursive function defined on a compact interval has a continuous second derivative, then it has a recursive first derivative [Computability and noncomputability in classical analysis, TAMS 275 (1983), 539-560, MR0682717].
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John Myhill gives an example of a recursive function defined on a compact interval and having a continuous derivative that is not recursive [Michigan Math. J. 18 (1971), 97-98]97-98, MR0280373]. However, Pour-El and Richards have shown that if a recursive function defined on a compact interval has a continuous second derivative, then it has a recursive first derivative [Computability and noncomputability in classical analysis, TAMS 275 (1983), 539-560]539-560, MR0682717]. |
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John Myhill gives an example of a recursive function defined on a compact interval and having a continuous derivative that is not recursive [Michigan Math. J. 18 (1971), 97-98]. However, Pour-El and Richards have shown that if a recursive function defined on a compact interval has a continuous second derivative, then it has a recursive first derivative [TAMS 275 (1983), 539-560]. |
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