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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
Posted:
June 26, 2007
MathSciNet review:
2338363
Full-text PDF
References |
Similar Articles |
Additional Information
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- [A]
- R. Apéry, Irrationalité de et , 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.
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- G. H. Hardy, Divergent series, Oxford, 1973. MR 0030620 (11:25a)
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- Omar Hijab, Introduction to Calculus and Classical Analysis, Springer, 2007 (Second Edition). MR 1449395 (98e:26001)
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- M. Kontsevich and D. Zagier, Periods, in 2001 and Beyond, 771-808, Springer, 2001. MR 1852188 (2002i:11002)
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- T. Rivoal, Irrationalité d'au moins un des neuf nombres
 , Acta Arith. 103 (2002), no. 2, 157-167. MR 1904870 (2003b:11068)
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- 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
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- 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:
http://dx.doi.org/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 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.
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