Evolutio producti infiniti (1–x)(1–xx)(1–x³)(1–x⁴)(1–x⁵)(1–x⁶) etc. in seriem simplicem

English Title

The expansion of the infinite product (1–x)(1–xx)(1–x³)(1–x⁴)(1–x⁵)(1–x⁶) etc. into a single series

Authors

Leonhard Euler

Enestrom Number

541

Fuss Index

167

Original Language

Latin

Content Summary

This paper does exactly what the title says it does. It expands the given series to arrive at the familiar "pentagonal number" expansion, now known as the pentagonal number theorem, and recalls its application to partition numbers. (Based on Jordan Bell's translation abstract.)

Published as

Journal article

Published Date

1783

Written Date

1775

Original Source Citation

Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 1780: I, pp. 47-55.

Opera Omnia Citation

Series 1, Volume 3, pp.472-479.

Record Created

2018-09-25