A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers
Euler gives a continued fraction representation for (1+x)n involving 1, 3, 5, 7, ..., and n2–1, n2–4, n3–9, ..., and squares of z, for x=2y and y=z/(1–z). He evaluates this continued fraction at z=tâ-1, for "vanishing" n, and for infinite n.
Original Source Citation
Mémoires de l'académie des sciences de St.-Petersbourg, Volume 6, pp. 3-11.
Opera Omnia Citation
Series 1, Volume 16B, pp.232-240.