E25 -- Methodus generalis summandi progressiones
(A general method for summing series)
This paper leads to Bernoulli numbers from an integral of an infinite series and is called a beautiful triumph by Euler.
the records, it was presented to the St. Petersburg Academy on June 20, 1732.
Originally published in Commentarii academiae scientiarum Petropolitanae 6, 1738, pp. 68-97
Opera Omnia: Series 1, Volume 14, pp. 42 - 72
- Reprinted in Comment. acad. sc. Petrop. 6, ed. nova, Bononiae 1743, pp. 61-94 [E25a]
- Original publication: E025 (in the Commentarii)
- Ian Bruce has translated E25 into English.
- 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 E25 include:
- Calinger R., “Leonhard Euler: The first St Petersburg years (1727-1741).” Historia Mathematica, 23 (2), pp. 121-166 (May 1996).
- 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).
- Ferraro G, Panza, M., “Developing into series and returning from series: A note on the foundations of eighteenth-century analysis.” Historia Mathematica, 30 (1), pp. 17-46 (Feb 2003).
- Ferraro G., “Some aspects of Euler's theory of series: Inexplicable functions and the Euler-Maclaurin summation formula.” Historia Mathematica, 25 (3), pp. 290-317 (Aug 1998).
- Grabiner JV., “Was Newton's calculus a dead end? The continental influence of Maclaurin's treatise of fluxions.” American Mathematical Monthly, 104 (5), pp. 393-410 (May 1997).
- Mills S., “The independent derivations by Euler, Leonhard and Maclaurin, Colin of the Euler-Maclaurin summation formula.” Archive for History of Exact Sciences, 33 (1-3), pp. 1-13 (1985).
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