Summatio progressionum sin(φ^λ) + sin(2φ^λ) + sin(3φ^λ) + ... + sin(nφ^λ); cos(φ^λ) + cos(2φ^λ) + cos(3φ^λ) + ... + cos(nφ^λ)

English Title

The summation of the progressions sin(φ^λ) + sin(2φ^λ) + sin(3φ^λ) + ... + sin(nφ^λ); cos(φ^λ) + cos(2φ^λ) + cos(3φ^λ) + ... + cos(nφ^λ)

Authors

Leonhard Euler

Enestrom Number

447

Fuss Index

182

Original Language

Latin

Content Summary

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.

Published as

Journal article

Published Date

1774

Written Date

1773

Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 18, pp. 24-36.

Opera Omnia Citation

Series 1, Volume 15, pp.168-184.

Record Created

2018-09-25