Weierstrass function (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Weierstrass function" in English language version.

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ams.org

See also: Brian R. Hunt (1998), "The Hausdorff dimension of graphs of Weierstrass functions", Proceedings of the American Mathematical Society, vol. 126, no. 3, pages 791–800.

mathscinet.ams.org

Zygmund, A. (2002) [1935]. Trigonometric Series. Cambridge Mathematical Library. Vol. I, II (3rd ed.). Cambridge University Press. p. 47. ISBN 978-0-521-89053-3. MR 1963498.

arxiv.org

Shen Weixiao (2018). "Hausdorff dimension of the graphs of the classical Weierstrass functions". Mathematische Zeitschrift. 289 (1–2): 223–266. arXiv:1505.03986. doi:10.1007/s00209-017-1949-1. ISSN 0025-5874. S2CID 118844077.

books.google.com

On page 560 of the 1872 Monatsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin (Monthly Reports of the Royal Prussian Academy of Science in Berlin), there is a brief mention that on 18 July, "Hr. Weierstrass las über stetige Funktionen ohne bestimmte Differentialquotienten" (Mr. Weierstrass read [a paper] about continuous functions without definite [i.e., well-defined] derivatives [to members of the Academy]). However, Weierstrass's paper was not published in the Monatsberichte.
Karl Weierstrass, "Über continuirliche Functionen eines reellen Arguments, die für keinen Werth des letzeren einen bestimmten Differentialquotienten besitzen" [On continuous functions of a real argument which possess a definite derivative for no value of the argument], in: Königlich Preussichen Akademie der Wissenschaften, Mathematische Werke von Karl Weierstrass (Berlin, Germany: Mayer & Mueller, 1895), vol. 2, pages 71–74.
See also: Karl Weierstrass, Abhandlungen aus der Functionenlehre [Treatises from the Theory of Functions] (Berlin, Germany: Julius Springer, 1886), page 97.

doi.org

Shen Weixiao (2018). "Hausdorff dimension of the graphs of the classical Weierstrass functions". Mathematische Zeitschrift. 289 (1–2): 223–266. arXiv:1505.03986. doi:10.1007/s00209-017-1949-1. ISSN 0025-5874. S2CID 118844077.
Gerver, Joseph (1969). "The Differentiability of the Riemann Function at Certain Rational Multiples of π". Proceedings of the National Academy of Sciences of the United States of America. 62 (3): 668–670. doi:10.1073/pnas.62.3.668. PMC 223649. PMID 16591735.
Gerver, Joseph (1971). "More on the Differentiability of the Riemann Function". American Journal of Mathematics. 93 (1): 33–41. doi:10.2307/2373445. JSTOR 2373445. S2CID 124562827.
Mazurkiewicz, S.. (1931). "Sur les fonctions non-dérivables". Studia Math. 3 (3): 92–94. doi:10.4064/sm-3-1-92-94.
Banach, S. (1931). "Über die Baire'sche Kategorie gewisser Funktionenmengen". Studia Math. 3 (3): 174–179. doi:10.4064/sm-3-1-174-179.

jstor.org

Gerver, Joseph (1971). "More on the Differentiability of the Riemann Function". American Journal of Mathematics. 93 (1): 33–41. doi:10.2307/2373445. JSTOR 2373445. S2CID 124562827.

nautil.us

Kucharski, Adam (26 October 2017). "Math's Beautiful Monsters: How a destructive idea paved the way for modern math". Retrieved 11 October 2023.

nih.gov

ncbi.nlm.nih.gov

Gerver, Joseph (1969). "The Differentiability of the Riemann Function at Certain Rational Multiples of π". Proceedings of the National Academy of Sciences of the United States of America. 62 (3): 668–670. doi:10.1073/pnas.62.3.668. PMC 223649. PMID 16591735.

pubmed.ncbi.nlm.nih.gov

Gerver, Joseph (1969). "The Differentiability of the Riemann Function at Certain Rational Multiples of π". Proceedings of the National Academy of Sciences of the United States of America. 62 (3): 668–670. doi:10.1073/pnas.62.3.668. PMC 223649. PMID 16591735.

semanticscholar.org

api.semanticscholar.org

Shen Weixiao (2018). "Hausdorff dimension of the graphs of the classical Weierstrass functions". Mathematische Zeitschrift. 289 (1–2): 223–266. arXiv:1505.03986. doi:10.1007/s00209-017-1949-1. ISSN 0025-5874. S2CID 118844077.
Gerver, Joseph (1971). "More on the Differentiability of the Riemann Function". American Journal of Mathematics. 93 (1): 33–41. doi:10.2307/2373445. JSTOR 2373445. S2CID 124562827.

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. "Weierstrass Function". MathWorld.

worldcat.org

search.worldcat.org

Shen Weixiao (2018). "Hausdorff dimension of the graphs of the classical Weierstrass functions". Mathematische Zeitschrift. 289 (1–2): 223–266. arXiv:1505.03986. doi:10.1007/s00209-017-1949-1. ISSN 0025-5874. S2CID 118844077.