English Title

Analytical observations

Authors

Leonhard Euler

Enestrom Number

553

Fuss Index

94

Original Language

Latin

Published as

Collection article

Published Date

1783

Written Date

1772

Content Summary

Euler seems to be expanding functions into continued fractions of functions. He begins 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)).

Original Source Citation

Opuscula analytica, Volume 1, pp. 85-120.

Opera Omnia Citation

Series 1, Volume 15, pp.400-434.

Record Created

2018-09-25

Included in

Mathematics Commons

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