Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
 Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Euler and his work on infinite series

Author(s): V. S. Varadarajan
Journal: Bull. Amer. Math. Soc. 44 (2007), 515-539.
MSC (2000): Primary 01A50, 40G10, 11M99
Posted: June 26, 2007
MathSciNet review: 2338363
Retrieve article in: PDF

References | Similar articles | Additional information

References:

[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
Email: vsv@math.ucla.edu

DOI: 10.1090/S0273-0979-07-01175-5
PII: S 0273-0979(07)01175-5
Received by editor(s): April 20, 2007
Received by editor(s) in revised form: April 23, 2007
Posted: June 26, 2007
Dedicated: For the 300th anniversary of Leonhard Euler's birth
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia