On the remarkable properties of the pentagonal numbers
Euler considers properties of the pentagonal numbers, those numbers of the form (3n2Â±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.