Notations For Continued Fractions
The integers a0, a1 etc., are called the quotients of the continued fraction. One can abbreviate the continued fraction
as
- ,
or in the notation of Pringsheim as
- ,
or in another related notation as
Sometimes angle brackets are used, like this:
The semicolon in the square and angle bracket notations is sometimes replaced by a comma.
One may also define infinite simple continued fractions as limits:
This limit exists for any choice of a0 and positive integers a1, a2, ... .
Read more about this topic: Continued Fraction
Famous quotes containing the word continued:
“Though the Jazz Age continued it became less and less an affair of youth. The sequel was like a children’s party taken over by the elders.”
—F. Scott Fitzgerald (1896–1940)