De transformatione seriei divergentis 1 – mx + m(m+n)x² – m(m+n)(m+2n)x³ + etc. in fractionem continuam

English Title

On the transformation of the divergent series 1 – mx + m(m+n)x² – m(m+n)(m+2n)x³ + etc. into a continued fraction

Authors

Leonhard Euler

Enestrom Number

616

Fuss Index

164

Original Language

Latin

Content Summary

In this paper, Euler transforms the divergent series in the title, and thereby derives a continued fraction expansion for π /4, namely π /4 = 1/(1+1/(2+9/(2+25/(2+49/(2+81/(2+⋯)))))).

Published as

Journal article

Published Date

1788

Written Date

1776

Original Source Citation

Nova Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 2, pp. 36-45.

Opera Omnia Citation

Series 1, Volume 16A, pp.34-46.

Record Created

2018-09-25