Euler's De Serie Lambertina (E532) English Translation
The original De Serie Lambertina (sometimes cited as De Serie Lambertine ) is available from this link . It is Enestrom number E532. This paper was written around 1776 and published around 1779 (Acta Academiae Scientiarum Imperialis Petropolitanae, Volume 1779: II, pp. 29-51), or 1783, depending on the reference. Euler reviews the results of Johann Heinrich Lambert's 1758 work Observationes Variae in Mathesin Puram (Various observation on pure mathematics) in Acta Helvetica Physico-Mathematico-Botanico-Medica (specifically, Acta Helvetica Vol III pp. 128-168, available here from Biodiversity Heritage Library ; I extracted the article as a PDF here on Google Drive ). I'll be reviewing the mathematics involved in this in a future post, but some details are available from this link , an answer of mine on History of Math and Science StackExchange. The equation considered by Euler is a trinomial symmetric in two parameters, α and β. (This is in contrast to Lambert's equation,