E553  Observationes analyticae
(Analytical observations)
Summary:
Euler seems to be expanding functions into continued fractions of functions. He starts with
f(x, y) and finds f(x, y) = A(x, y) +
P(y)/f(x, y + 1), where A is a linear function. He does it again in the
denominator, finding more linear functions B and C so that f(x, y) =
B(x, y) + Q(x)/(C(x, y) + f(x + 1, y)).
According to the records, it was presented to the St. Petersburg Academy on May 18, 1772.
Publication:

Originally published in Opuscula Analytica 1, 1783, pp. 85120.

Opera Omnia: Series 1, Volume 15, pp. 400  434
Documents Available:
 Original publication: E553
 German Translation (Alexander Aycock and Arseny Skryagin): E553
 Other works that cite this paper include:
Return to the Euler Archive