Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



Euler and his work on infinite series

Author: V. S. Varadarajan
Journal: Bull. Amer. Math. Soc. 44 (2007), 515-539
MSC (2000): Primary 01A50, 40G10, 11M99
Published electronically: June 26, 2007
MathSciNet review: 2338363
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [A] R. Apéry, Irrationalité de $ \zeta (2)$ et $ \zeta (3)$, Astérisque 61 (1979), 11-13.
  • [Bo] E. Borel, Leçons sur les Séries Divergentes, Éditions Jacques Gambay, 1988 (Reprinting of the original 1928 work).
  • [BL] E. J. Barbeau, and P. J. Leah, Euler's 1760 paper on divergent series, Historia Mathematica, 3(1976), 141-160. MR 0504847 (58:21162a)
  • [BR] K. Ball and T. Rivoal, Irrationalité d'une infinité de valeurs de la fonction zeta aux entiers impairs, Invent. Math. 146(2001), no. 1, 193-207. MR 1859021 (2003a:11086)
  • [C] P. Cartier, Mathemagics $ ($A Tribute to L. Euler and R. Feynman$ )$, Lecture Notes in Phys., vol. 550, Springer, Berlin, 2000, 6-67. MR 1861978 (2003c:81002)
  • [Ca] B. Candelpergher, J. C. Nosmas, and F. Pham, Approche de la résurgence, Hermann, Paris, 1993. MR 1250603 (95e:34005)
  • [D] P. Deligne, Letters $ ($Personal communication$ )$.
  • [D1] P. Deligne, Lectures at UCLA, Spring 2005.
  • [DV] T. Digernes and V. S. Varadarajan, Notes on Euler's continued fractions (In preparation).
  • [E] L. Euler, Omnia Opera. All of Euler's papers in pure mathematics are in Series I of his Omnia Opera. For most of the questions discussed here, see I-8, I-14, I-15.
  • [E1] L. Euler, De seriebus divergentibus, Opera Omnia, I, 14, 585-617.
  • [Ha] G. H. Hardy, Divergent series, Oxford, 1973. MR 0030620 (11:25a)
  • [Hi] Omar Hijab, Introduction to Calculus and Classical Analysis, Springer, 2007 (Second Edition). MR 1449395 (98e:26001)
  • [KZ] M. Kontsevich and D. Zagier, Periods, in 2001 and Beyond, 771-808, Springer, 2001. MR 1852188 (2002i:11002)
  • [P] H. Poincaré, Sur les intégrales des équations linéaires, Acta Math. 8(1886), 295-344; Oeuvres, TI, Gauthier-Villars (1928), 290-332. MR 1554701
  • [R] T. Rivoal, Irrationalité d'au moins un des neuf nombres $ \zeta(5),\zeta(7),\dots,\zeta(21)$, Acta Arith. 103 (2002), no. 2, 157-167. MR 1904870 (2003b:11068)
  • [V] V. S. Varadarajan, Euler Through Time: A New Look at Old Themes, AMS, 2006. This is a partial source for almost all the matters discussed and the references for works mentioned in this article. MR 2219954
  • [V1] V. S. Varadarajan, Linear meromorphic differential equations: a modern point of view. Bull. Amer. Math. Soc. (N.S.) 33 (1996), no. 1, 1-42. MR 1339809 (96h:34011)

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 01A50, 40G10, 11M99

Retrieve articles in all journals with MSC (2000): 01A50, 40G10, 11M99

Additional Information

V. S. Varadarajan
Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-1555

Received by editor(s): April 20, 2007
Received by editor(s) in revised form: April 23, 2007
Published electronically: June 26, 2007
Dedicated: For the 300$^{th}$ anniversary of Leonhard Euler’s birth
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society