De seriebus divergentibus

English Title

On divergent series

Authors

Leonhard Euler

Enestrom Number

247

Fuss Index

125

Original Language

Latin

Content Summary

One feature of this article is an evaluation of the hypergeometric series 1 – 1 + 2 – 6 + 24 – 120 + 720 ± …, by looking at the function s(x) = x – x² + 2!∙x³ – 3!∙x⁴ + 4!∙x⁵ – 5!∙x⁶ ± .... Euler uses interpolation methods to get an answer around 0.59. Then he integrates it and evaluates again by continued fractions, and gets the much more precise value of 0.5963473621372.

Published as

Journal article

Published Date

1760

Written Date

1746

Original Source Citation

Novi Commentarii academiae scientiarum Petropolitanae, Volume 5, pp. 205-237.

Opera Omnia Citation

Series 1, Volume 14, pp.585-617.

Record Created

2018-09-25