E72 -- Variae observationes circa series infinitas
(Various observations about infinite series)
Summary:
This is the paper in which Euler product expansions first appeared.
In the Enestrom Index, it is recorded that E72 was presented to the St. Petersburg
Academy on April 25, 1727. (Probably this is a typo, and should read 1737.)
Publication:
-
Originally published in Commentarii academiae scientiarum Petropolitanae 9, 1744, pp. 160-188
-
Opera Omnia: Series 1, Volume 14, pp. 217 - 244
- A handwritten French translation of this treatise can be found in the library of the observatory in
Uccle, near Brussels.
Documents Available:
- Original publication: E072
(in the Commentarii)
- A translation of E72
into English by Pelegri Viader (Universitat Pompeu Fabra, Barcelona) and
Lluis Bibiloni (Universitat Autonoma de Barcelona, Barcelona) is available.
- The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E72 include:
- Burdick, B. and Sandifer, E. "Fooling with an Euler Series." International Journal of Mathematics and Computer Science 4 (2009), no. 1. Burdick and Sandifer present a formal proof of Euler's Theorem 1.
- Diamond HG., “Elementary methods in the study of the distribution of prime-numbers.” Bulletin of the American Mathematical Society, 7 (3), pp. 553-589 (1982).
- Dutka J., “On the summation of some divergent series of Euler and the zeta functions.” Archive for History of Exact Sciences, 50 (2), pp. 187-200 (1996).
- Hughes CP., "On the Characteristic Polynomial of a Random Unitary Matrix
and the Riemann Zeta Function," in pdf format
- Sandifer E., "Goldbach series." How Euler Did It. (Published online
by the MAA.)
- Sandifer E., "Infinitely many primes." How Euler Did It. (Published online
by the MAA.)
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