Riemann’s example of a continuous “nondifferentiable” function continued

@article{Segal1978RiemannsEO,
  title={Riemann’s example of a continuous “nondifferentiable” function continued},
  author={Sanford L. Segal},
  journal={The Mathematical Intelligencer},
  year={1978},
  volume={1},
  pages={81-82}
}
  • S. Segal
  • Published 1 June 1978
  • Mathematics
  • The Mathematical Intelligencer
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References

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The functiong(x)= :P%-= (sin 7rp2X/7rp2), thought by Riemann to be nowhere differentiable, is shown to be differentiable only at rational points expressible as the ratio of odd integers. The proof
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THE DIFFERENTIABILITY OF THE RIEMANN FUNCTION AT CERTAIN RATIONAL MULTIPLES OF pi.
  • J. Gerver
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1969
It is shown that a continuous function which Riemann is said to have believed to be nowhere differentiable is in fact differentiable at certain points.
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where X is an odd integer à 3, and a a positive number such that a < 1 and aX>l+37r /2 : (2) is a continuous function which is nowhere differentiable [49]. Later on, Weierstrass's result was improved