The summation of the progressions sin(φλ) + sin(2φλ) + sin(3φλ) + ... + sin(nφλ); cos(φλ) + cos(2φλ) + cos(3φλ) + ... + cos(nφλ)
This paper begins much like E246, with the substitutions of u and v into an infinite series. They diverge if λ>1. As Enlin Pan points out in his commentary, though, there is more going on here. Before the paper is over, Euler generalizes the notion of limit, and comes quite close to developing the basic ideas of Fourier series and Cesàro sums.
Original Source Citation
Novi Commentarii academiae scientiarum Petropolitanae, Volume 18, pp. 24-36.
Opera Omnia Citation
Series 1, Volume 15, pp.168-184.