E477 -- Meditationes circa singulare serierum genus
(Meditations about a singular type of series)
Summary:
Euler shows that sm, n = 1 + (1/2m)(1 + 1/2n) + (1/3m)(1 + 1/2n + 1/3n) + (1/4m)(1 + 1/2n + 1/3n + 1/4n) + ...
and sn = sn, 0. He gets a relation sn, n = ½ sn2 + ½ s2n, along with some similar, more complicated formulas. Then he evaluates sm, n for m + n = 6.
According to the records, it was presented to the St. Petersburg Academy on July 4, 1771.
Publication:
-
Originally published in Novi Commentarii academiae scientiarum Petropolitanae 20, 1776, pp. 140-186
-
Opera Omnia: Series 1, Volume 15, pp. 217 - 267
Documents Available:
- Original publication: E477
- Alexander Aycock has made draft translations into German and English, available online at Euler-Kreis Mainz.
Return to the Euler Archive