Variae observationes circa angulos in progressione geometrica progredientes

English Title

Various observations about angles proceeding in geometric progression

Authors

Leonhard Euler

Enestrom Number

561

Fuss Index

153

Original Language

Latin

Content Summary

From the identity sin(s) = 2 sin(s/2) cos(s/2), Euler obtains the infinite product formula sin(s) = s cos(s/2) cos(s/4) cos(s/8) cos(s/16).... He divides by the infinite product and applies logarithmic differentiation to get an infinite sum for 1/s involving cotangents and tangents.

Published as

Collection article

Published Date

1783

Written Date

1773

Original Source Citation

Opuscula analytica, Volume 1, pp. 345-352.

Opera Omnia Citation

Series 1, Volume 15, pp.498-508.

Record Created

2018-09-25