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:
“Along the journey we commonly forget its goal. Almost every vocation is chosen and entered upon as a means to a purpose but is ultimately continued as a final purpose in itself. Forgetting our objectives is the most frequent stupidity in which we indulge ourselves.”
—Friedrich Nietzsche (1844–1900)