E553 -- Observationes analyticae

(Analytical observations)


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.

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