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Bulletin of the American Mathematical Society
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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
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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)


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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.


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