On the sums of series of reciprocals
According to Eneström, this paper was not handed in after its presentation at the St. Petersburg Academy.
Euler finds the values of ζ(2n), where ζ is now named as the Riemann zeta function. He introduces the Euler numbers En. All the odd-indexed Euler numbers are zero, E0=1, E2=-1, E4=5, E6=-61, E8=1380, and they satisfy (E+1)n + (E-1)n = 0. (The Euler numbers are the coefficients of the series expansion of sech(x) and are related to Bernoulli numbers.) Among other things, this paper includes an infinite product formula for sin(x)/x.
Original Source Citation
Commentarii academiae scientiarum Petropolitanae, Volume 7, pp. 123-134.
Opera Omnia Citation
Series 1, Volume 14, pp.73-86.