E750  Commentatio in fractionem continuam, qua illustris La Grange potestates binomiales expressit
(A commentary on the continued fraction by which the illustrious La Grange has expressed the binomial powers)
Summary:
Euler gives a continued fraction representation of (1 + x)^{n}.
involving 1,3,5,7,... and n^21,n^24,n^39,...
and squares of z, for x=2y and y=z/(1z). He evaluates this continued fraction at z=t sqrt(1), for ``vanishing''
n, and for infinite n.
Publication:

riginally published in Mémoires de l'académie des sciences de St.Petersbourg 6, 1818, pp. 311

Opera Omnia: Series 1, Volume 16, pp. 232  240
Documents Available:
 Original Publication: E750
 English translation (Jordan Bell): E750
 German translation (Artur Diener and Alexander Aycock): E750
 The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E750 include:
 Ku YH., “Solution of Riccati equation by continued fractions.” Journal of the Franklin InstituteEngineering and Applied Mathematics, 293 (1), pp. 59& (1972).
 Eric Weisstein's definition of natural logarithm, available here.
Return to the Euler Archive