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:
“There is not any present moment that is unconnected with some future one. The life of every man is a continued chain of incidents, each link of which hangs upon the former. The transition from cause to effect, from event to event, is often carried on by secret steps, which our foresight cannot divine, and our sagacity is unable to trace. Evil may at some future period bring forth good; and good may bring forth evil, both equally unexpected.”
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