Mathematische Annalen

, Volume 65, Issue 3, pp 350–369 | Cite as

On the limits of certain infinite series and integrals

  • T. J. I. Bromwich


Infinite Series 
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  1. L. Fejér, Math. Annalen, Bd. 58, 1904, p. 51. G. H. Hardy, Proc. Lond. Math. Soc. (2), vol. 3, 1906, p. 247; and Math. Annalen, Bd. 64, 1907, p. 77. C. N. Moore, Trans. Amer. Math. Soc. vol. 8, 1907, p. 299.Google Scholar
  2. See E. Landau, Münchener Sitzungsberichte Bd. 36, 1906, pp. 157, 160.Google Scholar
  3. Trans. Amer. Math. Society, vol. 8, April 1907, p. 300.Google Scholar
  4. Math. Annalen, Bd. 64, p. 78.Google Scholar
  5. See p. 86 of the paper quoted.Google Scholar
  6. Math. Annalen, Bd. 58, p. 62.Google Scholar
  7. See p. 88 of the paper quoted.Google Scholar
  8. Bulletin des Sciences mathématiques (2), t. 14, 1890, p. 114; the definition of „une série k fois indéterminée” is given on p. 119. See also Borel, Séries Divergentes p. 91, where, however, the precise definition is not elaborated for higher values thank=1. The reader may also consult Cesàro, „Sulla determinazione assintotica delle serie di potenze” Rendiconti della R. Accademia delle Scienze fisiche e matematiche di Napoli 28 ottobre 1893; and Bromwich, Infinite Series (London, 1908), Arts. 122–129.Google Scholar
  9. Mathematische Annalen, Bd. 20, 1882, p. 535.Google Scholar
  10. Stolz, Mathematische Annalen, Bd. 14, 1879, p. 234; Allgemeine Arithmetik, Bd. 1, p. 173. Bromwich, Infinite Series, p. 378.Google Scholar
  11. Inauguraldissertation, Berlin 1907, p. 19–23; this dissertation reached me during the investigations given here. I had already obtained Dr. Knopp's result fork=3 but had not established it in general.Google Scholar

Copyright information

© Springer-Verlag 1908

Authors and Affiliations

  • T. J. I. Bromwich
    • 1
  1. 1.CambridgeEngland

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