aequationes mathematicae

, Volume 34, Issue 2–3, pp 264–276 | Cite as

Hidden lemmas in the early history of infinite series

  • D. Laugwitz
Research Papers

Abstract

Euler, Fourier, Poisson and Cauchy appear to have used, in a more or less implicit form, some facts on infinitely small quantities. Attempting to state and prove several lemmata, I shall discuss their relationships to interchanges of limits in series and integrals. Early methods of summation for divergent series and integrals, including a conjecture of Poisson, are discussed.

AMS (1980) subject classification

Primary 01A99 Secondary 03H05, 40A05 

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Copyright information

© Birkhäuser Verlag 1987

Authors and Affiliations

  • D. Laugwitz
    • 1
  1. 1.Fachbereich MathematikTechnische Hochschule DarmstadtDarmstadtWest Germany

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