E55 Methodus universalis series summandi ulterius promota (Universal method for summation of series, further developed)
Summary:
This, along with , looks at the formal series f a f a+h f a h f a h f a h )-.... He apparently looks at this also in , as well as in . He looks at this through a power series, f f x f x f x + ..., which is obviously what hes looking for in the case a h =1 and x =-1. He does Taylor series expansions at every value, 0, 1, 2,... , sums them all, and combines terms and gets an answer that reminds Faber of
According to the records, it was presented to the St. Petersburg Academy on September 17, 1736.
Publication: - Originally published in Commentarii academiae scientiarum Petropolitanae 8, 1741, pp. 147-158
- Opera Omnia : Series 1, Volume 14, pp. 124 - 137
- Reprinted in Comment. acad. sc. Petrop . 8, ed. nova, Bononiae 1752, pp. 132-144 [55a]
Documents Available: - Original publication: (in the Commentarii
- 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 E55 include:
- Apostol TM., An elementary view of Euler's summation formula. American Mathematical Monthly, 106 (5), pp. 409-418 (May 1999).
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