Advertisement

The Mathematical Intelligencer

, Volume 28, Issue 3, pp 4–5 | Cite as

An elementary proof of the Gregory-Mengoli-Mercator formula

  • Gero Friesecke
  • Jan Christoph Wehrstedt
Department Note
  • 92 Downloads

Keywords

Elementary Proof Quadrature Problem Harmonic Series Power Series Representation Richard Courant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Refferences

  1. [A]
    Niels Henrik Abel, Recherches sur la serie\(1 + \frac{m}{1}X + \frac{{m(m + 1)}}{{1 \cdot 2}}X^2 + \frac{{m(m + 1)(m + 2)}}{{1 \cdot 2 \cdot 3}}X^3 + \ldots \), CreteJournal 1, 311–339, 1827. Reprinted in L. Sylow & S. Lie (eds),Oeuvres complètes de N. H. Abel, Tome 1, 219-250, Grondell & Son, 1881.Google Scholar
  2. [C]
    Richard Courant,Vorlesungen über Differential- und Integralrechnung. Erster Band. Springer 1955Google Scholar
  3. [G]
    James Gregory,Vera Circuli et Hyperbolae Quadratura, in Propria Sua Proportionis Specie, Inventa & Demonstrata, Padua, 1667.Google Scholar
  4. [H]
    Stefan Hildebrandt,Analysis 1, Springer, 2002Google Scholar
  5. [K]
    Max Koecher,Klassiche elementare Analysis, Birkhäuser, 1987.Google Scholar
  6. [Men]
    Pietro Mengoli,Novae quadraturae arithmeticae, seu de additione fractionum. Bologna 1650.Google Scholar
  7. [Mer]
    Nicolaus Mercator,Logarithmotechnia, 1668.Google Scholar
  8. [R]
    Walter Rudin,Principles of Mathematical Analysis, 2nd edition, McGraw-Hill, 1964Google Scholar

Copyright information

© Springer Science + Business Media Inc. 2006

Authors and Affiliations

  1. 1.Zentrum Mathematik Technische Universität MünchenGarching b. MünchenGermany
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

Personalised recommendations