English Title

Elucidations about the formula, in which the sines and cosines of angles are to be multiplied, where at once large difficulties are diluted

Authors

Leonhard Euler

Enestrom Number

686

Fuss Index

148

Original Language

Latin

Published as

Journal article

Published Date

1795

Written Date

1777

Content Summary

Euler begins by deriving a polynomial expansion for 2 cos(nφ). He then substitutes z for cos(φ) and s = cos(nφ) and obtains a second order differential equation. He tries to solve that with unknown coefficients and gets another series for cos(nφ).

Original Source Citation

Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 9, pp. 54-80.

Opera Omnia Citation

Series 1, Volume 16A, pp.282-310.

Record Created

2018-09-25

Included in

Mathematics Commons

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