English Title

On the remarkable properties of the pentagonal numbers

Authors

Leonhard Euler

Enestrom Number

542

Fuss Index

36

Original Language

Latin

Published as

Journal article

Published Date

1783

Written Date

1775

Content Summary

Euler considers properties of the pentagonal numbers, those numbers of the form (3n2±n)/2. He starts with the series in E541 and notices that some of its exponents are pentagonal numbers. He then tries to substitute the roots of the infinite product into the series. (Based on Jordan Bell's translation abstract.)

Original Source Citation

Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 1780: I, pp. 56-75.

Opera Omnia Citation

Series 1, Volume 3, pp.480-496.

Record Created

2018-09-25

Included in

Mathematics Commons

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